Monday, November 18, 2024
Sunday, November 10, 2024
Wednesday, November 06, 2024
Monday, November 04, 2024
Sunday, October 27, 2024
Sunday, October 20, 2024
Friday, October 18, 2024
Friday, October 04, 2024
Breather
I have today finished examining the Leyland numbers from 1000800 digits to 1000899 digits and have found no PRPs therein. This adds to my previous search of 1000900 digits to 1000999 digits completed 26 Jan 2024 wherein I found three PRPs. At nine to ten months per search, I am not anxious to try another such interval. Yesterday was the ninth (year) anniversary of my very first Leyland-prime find. That's a long time to be obsessed with the task. I'm going to take a breather.
Thursday, October 03, 2024
Éric Angelini (1951-2024)
Pascale SCHOENMAECKERS,
son épouse,
Cécile ANGELINI,
Lorenzo ANGELINI et Marie LE HENAFF,
ses enfants et sa belle-fille,
Domenico ANGELINI et Monica ANGELINI,
Catherine ANGELINI,
Letizia ANGELINI et Henri DEFRANCHI,
Marina ANGELINI et Éric VAN NEROM,
son frère et ses soeurs,
Bidè,
son compère,
Les familles ANGELINI et apparentées,
ont la tristesse d’annoncer le décès de
MONSIEUR
Éric ANGELINI
né à Ostende le 12 septembre 1951
et décédé à Uccle le 27 septembre 2024.
Le service, suivi de l’inhumation au cimetière d’Ixelles,
aura lieu dans l’église Sainte-Anne à Uccle
le JEUDI 3 OCTOBRE 2024, à 10 h 30.
La famille y recevra les condoléances dès 10 heures.
Après avoir joué 1. e4, Éric aurait relevé que
le présent avis, qui tient lieu de faire-part,
comporte six cent septante-cinq signes jusqu’ici.
The above transliterated copy of the original obituary allows for two ligatures to be treated each as two "signes" in order to make the self-referential closing assertion true. Éric's final Cinquante signes article just misses Michael Branicky's (late Sep. 27) emailed response:
1 [length 0]
2 [length 8]
-> 2^2 = 4
-> 4^2 = 16
-> 1^2 + 6^2 = 37
-> 37^2 = 1369
-> 1^2 + 369^2 = 136162
-> 1^2 + 36^2 + 16^2 + 2^2 = 1557
-> 1^2 + 5^2 + 5^2 + 7^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
3 [length 7]
-> 3^2 = 9
-> 9^2 = 81
-> 81^2 = 6561
-> 6^2 + 56^2 + 1^2 = 3173
-> 3^2 + 1^2 + 7^2 + 3^2 = 68
-> 6^2 + 8^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
4 [length 7]
-> 4^2 = 16
-> 1^2 + 6^2 = 37
-> 37^2 = 1369
-> 1^2 + 369^2 = 136162
-> 1^2 + 36^2 + 16^2 + 2^2 = 1557
-> 1^2 + 5^2 + 5^2 + 7^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
5 [length 7]
-> 5^2 = 25
-> 25^2 = 625
-> 62^2 + 5^2 = 3869
-> 3^2 + 869^2 = 755170
-> 755^2 + 17^2 + 0^2 = 570314
-> 5^2 + 7^2 + 0^2 + 3^2 + 1^2 + 4^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
6 [length 6]
-> 6^2 = 36
-> 36^2 = 1296
-> 1296^2 = 1679616
-> 1679616^2 = 2821109907456
-> 28^2 + 21^2 + 1^2 + 0^2 + 9^2 + 9^2 + 0^2 + 74^2 + 56^2 = 10000
-> 1^2 + 0^2 + 0^2 + 0^2 + 0^2 = 1
7 [length 5]
-> 7^2 = 49
-> 4^2 + 9^2 = 97
-> 9^2 + 7^2 = 130
-> 1^2 + 3^2 + 0^2 = 10
-> 1^2 + 0^2 = 1
8 [length 5]
-> 8^2 = 64
-> 64^2 = 4096
-> 40^2 + 9^2 + 6^2 = 1717
-> 1^2 + 7^2 + 1^2 + 7^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
9 [length 6]
-> 9^2 = 81
-> 81^2 = 6561
-> 6^2 + 56^2 + 1^2 = 3173
-> 3^2 + 1^2 + 7^2 + 3^2 = 68
-> 6^2 + 8^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
10 [length 1]
-> 1^2 + 0^2 = 1
11 [length 6]
-> 11^2 = 121
-> 12^2 + 1^2 = 145
-> 1^2 + 45^2 = 2026
-> 2^2 + 0^2 + 26^2 = 680
-> 6^2 + 8^2 + 0^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
12 [length 6]
-> 12^2 = 144
-> 1^2 + 44^2 = 1937
-> 1^2 + 9^2 + 37^2 = 1451
-> 1^2 + 4^2 + 51^2 = 2618
-> 26^2 + 18^2 = 1000
-> 1^2 + 0^2 + 0^2 + 0^2 = 1
13 [length 2]
-> 1^2 + 3^2 = 10
-> 1^2 + 0^2 = 1
14 [length 6]
-> 1^2 + 4^2 = 17
-> 17^2 = 289
-> 289^2 = 83521
-> 8^2 + 3^2 + 5^2 + 2^2 + 1^2 = 103
-> 1^2 + 0^2 + 3^2 = 10
-> 1^2 + 0^2 = 1
15 [length 6]
-> 15^2 = 225
-> 225^2 = 50625
-> 5^2 + 0^2 + 625^2 = 390650
-> 390^2 + 65^2 + 0^2 = 156325
-> 1^2 + 5^2 + 6^2 + 3^2 + 2^2 + 5^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
16 [length 6]
-> 1^2 + 6^2 = 37
-> 37^2 = 1369
-> 1^2 + 369^2 = 136162
-> 1^2 + 36^2 + 16^2 + 2^2 = 1557
-> 1^2 + 5^2 + 5^2 + 7^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
17 [length 5]
-> 17^2 = 289
-> 289^2 = 83521
-> 8^2 + 3^2 + 5^2 + 2^2 + 1^2 = 103
-> 1^2 + 0^2 + 3^2 = 10
-> 1^2 + 0^2 = 1
18 [length 6]
-> 1^2 + 8^2 = 65
-> 65^2 = 4225
-> 4^2 + 225^2 = 50641
-> 50^2 + 641^2 = 413381
-> 4^2 + 1^2 + 3^2 + 3^2 + 8^2 + 1^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
19 [length 4]
-> 1^2 + 9^2 = 82
-> 8^2 + 2^2 = 68
-> 6^2 + 8^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
20 [length 7]
-> 20^2 = 400
-> 40^2 + 0^2 = 1600
-> 1^2 + 60^2 + 0^2 = 3601
-> 3601^2 = 12967201
-> 12967201^2 = 168148301774401
-> 16^2 + 8^2 + 1^2 + 48^2 + 3^2 + 0^2 + 17^2 + 74^2 + 40^2 + 1^2 = 10000
-> 1^2 + 0^2 + 0^2 + 0^2 + 0^2 = 1
21 [length 6]
-> 21^2 = 441
-> 4^2 + 41^2 = 1697
-> 1^2 + 6^2 + 9^2 + 7^2 = 167
-> 1^2 + 6^2 + 7^2 = 86
-> 8^2 + 6^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
22 [length 6]
-> 2^2 + 2^2 = 8
-> 8^2 = 64
-> 64^2 = 4096
-> 40^2 + 9^2 + 6^2 = 1717
-> 1^2 + 7^2 + 1^2 + 7^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
23 [length 3]
-> 2^2 + 3^2 = 13
-> 1^2 + 3^2 = 10
-> 1^2 + 0^2 = 1
24 [length 6]
-> 24^2 = 576
-> 57^2 + 6^2 = 3285
-> 3285^2 = 10791225
-> 10^2 + 7^2 + 9^2 + 1^2 + 2^2 + 25^2 = 860
-> 8^2 + 6^2 + 0^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
25 [length 6]
-> 25^2 = 625
-> 62^2 + 5^2 = 3869
-> 3^2 + 869^2 = 755170
-> 755^2 + 17^2 + 0^2 = 570314
-> 5^2 + 7^2 + 0^2 + 3^2 + 1^2 + 4^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
26 [length 6]
-> 26^2 = 676
-> 67^2 + 6^2 = 4525
-> 4^2 + 525^2 = 275641
-> 2^2 + 7^2 + 564^2 + 1^2 = 318150
-> 3^2 + 1^2 + 8^2 + 1^2 + 5^2 + 0^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
27 [length 5]
-> 27^2 = 729
-> 729^2 = 531441
-> 5^2 + 3^2 + 1^2 + 4^2 + 4^2 + 1^2 = 68
-> 6^2 + 8^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
28 [length 3]
-> 2^2 + 8^2 = 68
-> 6^2 + 8^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
29 [length 6]
-> 2^2 + 9^2 = 85
-> 85^2 = 7225
-> 7^2 + 2^2 + 2^2 + 5^2 = 82
-> 8^2 + 2^2 = 68
-> 6^2 + 8^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
30 [length 6]
-> 30^2 = 900
-> 90^2 + 0^2 = 8100
-> 810^2 + 0^2 = 656100
-> 6^2 + 5^2 + 610^2 + 0^2 = 372161
-> 3^2 + 7^2 + 2^2 + 1^2 + 6^2 + 1^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
31 [length 2]
-> 3^2 + 1^2 = 10
-> 1^2 + 0^2 = 1
32 [length 3]
-> 3^2 + 2^2 = 13
-> 1^2 + 3^2 = 10
-> 1^2 + 0^2 = 1
33 [length 6]
-> 33^2 = 1089
-> 1^2 + 0^2 + 89^2 = 7922
-> 7^2 + 922^2 = 850133
-> 85013^2 + 3^2 = 7227210178
-> 7^2 + 2^2 + 27^2 + 2^2 + 10^2 + 1^2 + 7^2 + 8^2 = 1000
-> 1^2 + 0^2 + 0^2 + 0^2 = 1
34 [length 5]
-> 34^2 = 1156
-> 1^2 + 15^2 + 6^2 = 262
-> 26^2 + 2^2 = 680
-> 6^2 + 8^2 + 0^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
35 [length 6]
-> 3^2 + 5^2 = 34
-> 34^2 = 1156
-> 1^2 + 15^2 + 6^2 = 262
-> 26^2 + 2^2 = 680
-> 6^2 + 8^2 + 0^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
36 [length 5]
-> 36^2 = 1296
-> 1296^2 = 1679616
-> 1679616^2 = 2821109907456
-> 28^2 + 21^2 + 1^2 + 0^2 + 9^2 + 9^2 + 0^2 + 74^2 + 56^2 = 10000
-> 1^2 + 0^2 + 0^2 + 0^2 + 0^2 = 1
37 [length 5]
-> 37^2 = 1369
-> 1^2 + 369^2 = 136162
-> 1^2 + 36^2 + 16^2 + 2^2 = 1557
-> 1^2 + 5^2 + 5^2 + 7^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
38 [length 5]
-> 38^2 = 1444
-> 144^2 + 4^2 = 20752
-> 207^2 + 52^2 = 45553
-> 4^2 + 5^2 + 5^2 + 5^2 + 3^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
39 [length 4]
-> 39^2 = 1521
-> 1^2 + 5^2 + 2^2 + 1^2 = 31
-> 3^2 + 1^2 = 10
-> 1^2 + 0^2 = 1
40 [length 6]
-> 40^2 = 1600
-> 1^2 + 60^2 + 0^2 = 3601
-> 3601^2 = 12967201
-> 12967201^2 = 168148301774401
-> 16^2 + 8^2 + 1^2 + 48^2 + 3^2 + 0^2 + 17^2 + 74^2 + 40^2 + 1^2 = 10000
-> 1^2 + 0^2 + 0^2 + 0^2 + 0^2 = 1
41 [length 6]
-> 4^2 + 1^2 = 17
-> 17^2 = 289
-> 289^2 = 83521
-> 8^2 + 3^2 + 5^2 + 2^2 + 1^2 = 103
-> 1^2 + 0^2 + 3^2 = 10
-> 1^2 + 0^2 = 1
42 [length 6]
-> 42^2 = 1764
-> 1^2 + 7^2 + 6^2 + 4^2 = 102
-> 102^2 = 10404
-> 1^2 + 0^2 + 404^2 = 163217
-> 1^2 + 6^2 + 3^2 + 2^2 + 1^2 + 7^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
43 [length 6]
-> 43^2 = 1849
-> 1^2 + 8^2 + 49^2 = 2466
-> 2^2 + 466^2 = 217160
-> 2^2 + 1^2 + 7^2 + 16^2 + 0^2 = 310
-> 3^2 + 1^2 + 0^2 = 10
-> 1^2 + 0^2 = 1
44 [length 4]
-> 4^2 + 4^2 = 32
-> 3^2 + 2^2 = 13
-> 1^2 + 3^2 = 10
-> 1^2 + 0^2 = 1
45 [length 6]
-> 45^2 = 2025
-> 20^2 + 25^2 = 1025
-> 10^2 + 2^2 + 5^2 = 129
-> 1^2 + 2^2 + 9^2 = 86
-> 8^2 + 6^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
46 [length 5]
-> 46^2 = 2116
-> 2116^2 = 4477456
-> 4^2 + 47^2 + 7^2 + 456^2 = 210210
-> 2^2 + 1^2 + 0^2 + 2^2 + 1^2 + 0^2 = 10
-> 1^2 + 0^2 = 1
47 [length 5]
-> 47^2 = 2209
-> 22^2 + 0^2 + 9^2 = 565
-> 5^2 + 6^2 + 5^2 = 86
-> 8^2 + 6^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
48 [length 5]
-> 48^2 = 2304
-> 230^2 + 4^2 = 52916
-> 5^2 + 29^2 + 16^2 = 1122
-> 1^2 + 1^2 + 2^2 + 2^2 = 10
-> 1^2 + 0^2 = 1
49 [length 4]
-> 4^2 + 9^2 = 97
-> 9^2 + 7^2 = 130
-> 1^2 + 3^2 + 0^2 = 10
-> 1^2 + 0^2 = 1
50 [length 6]
-> 50^2 = 2500
-> 2^2 + 50^2 + 0^2 = 2504
-> 25^2 + 0^2 + 4^2 = 641
-> 6^2 + 41^2 = 1717
-> 1^2 + 7^2 + 1^2 + 7^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
51 [length 6]
-> 51^2 = 2601
-> 2^2 + 60^2 + 1^2 = 3605
-> 3^2 + 605^2 = 366034
-> 366034^2 = 133980889156
-> 13^2 + 39^2 + 8^2 + 0^2 + 8^2 + 89^2 + 15^2 + 6^2 = 10000
-> 1^2 + 0^2 + 0^2 + 0^2 + 0^2 = 1
52 [length 5]
-> 52^2 = 2704
-> 2704^2 = 7311616
-> 731^2 + 1^2 + 6^2 + 1^2 + 6^2 = 534435
-> 5^2 + 3^2 + 4^2 + 4^2 + 3^2 + 5^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
53 [length 6]
-> 5^2 + 3^2 = 34
-> 34^2 = 1156
-> 1^2 + 15^2 + 6^2 = 262
-> 26^2 + 2^2 = 680
-> 6^2 + 8^2 + 0^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
54 [length 5]
-> 54^2 = 2916
-> 291^2 + 6^2 = 84717
-> 84^2 + 7^2 + 1^2 + 7^2 = 7155
-> 7^2 + 1^2 + 5^2 + 5^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
55 [length 5]
-> 55^2 = 3025
-> 302^2 + 5^2 = 91229
-> 9^2 + 12^2 + 2^2 + 9^2 = 310
-> 3^2 + 1^2 + 0^2 = 10
-> 1^2 + 0^2 = 1
56 [length 6]
-> 5^2 + 6^2 = 61
-> 61^2 = 3721
-> 3721^2 = 13845841
-> 1^2 + 38^2 + 4^2 + 58^2 + 4^2 + 1^2 = 4842
-> 4^2 + 8^2 + 4^2 + 2^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
57 [length 4]
-> 57^2 = 3249
-> 324^2 + 9^2 = 105057
-> 1^2 + 0^2 + 5^2 + 0^2 + 5^2 + 7^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
58 [length 5]
-> 58^2 = 3364
-> 3364^2 = 11316496
-> 113^2 + 16^2 + 4^2 + 9^2 + 6^2 = 13158
-> 1^2 + 3^2 + 1^2 + 5^2 + 8^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
59 [length 4]
-> 59^2 = 3481
-> 34^2 + 8^2 + 1^2 = 1221
-> 1^2 + 2^2 + 2^2 + 1^2 = 10
-> 1^2 + 0^2 = 1
60 [length 6]
-> 6^2 + 0^2 = 36
-> 36^2 = 1296
-> 1296^2 = 1679616
-> 1679616^2 = 2821109907456
-> 28^2 + 21^2 + 1^2 + 0^2 + 9^2 + 9^2 + 0^2 + 74^2 + 56^2 = 10000
-> 1^2 + 0^2 + 0^2 + 0^2 + 0^2 = 1
61 [length 5]
-> 61^2 = 3721
-> 3721^2 = 13845841
-> 1^2 + 38^2 + 4^2 + 58^2 + 4^2 + 1^2 = 4842
-> 4^2 + 8^2 + 4^2 + 2^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
62 [length 5]
-> 62^2 = 3844
-> 3844^2 = 14776336
-> 14776^2 + 3^2 + 3^2 + 6^2 = 218330230
-> 2^2 + 1^2 + 8^2 + 3^2 + 3^2 + 0^2 + 2^2 + 3^2 + 0^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
63 [length 5]
-> 63^2 = 3969
-> 3^2 + 969^2 = 938970
-> 9^2 + 3^2 + 89^2 + 7^2 + 0^2 = 8060
-> 8^2 + 0^2 + 6^2 + 0^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
64 [length 4]
-> 64^2 = 4096
-> 40^2 + 9^2 + 6^2 = 1717
-> 1^2 + 7^2 + 1^2 + 7^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
65 [length 5]
-> 65^2 = 4225
-> 4^2 + 225^2 = 50641
-> 50^2 + 641^2 = 413381
-> 4^2 + 1^2 + 3^2 + 3^2 + 8^2 + 1^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
66 [length 4]
-> 66^2 = 4356
-> 4^2 + 3^2 + 5^2 + 6^2 = 86
-> 8^2 + 6^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
67 [length 6]
-> 6^2 + 7^2 = 85
-> 85^2 = 7225
-> 7^2 + 2^2 + 2^2 + 5^2 = 82
-> 8^2 + 2^2 = 68
-> 6^2 + 8^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
68 [length 2]
-> 6^2 + 8^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
69 [length 5]
-> 6^2 + 9^2 = 117
-> 117^2 = 13689
-> 13689^2 = 187388721
-> 18^2 + 7^2 + 3^2 + 8^2 + 8^2 + 7^2 + 21^2 = 1000
-> 1^2 + 0^2 + 0^2 + 0^2 = 1
70 [length 5]
-> 7^2 + 0^2 = 49
-> 4^2 + 9^2 = 97
-> 9^2 + 7^2 = 130
-> 1^2 + 3^2 + 0^2 = 10
-> 1^2 + 0^2 = 1
71 [length 5]
-> 71^2 = 5041
-> 5^2 + 0^2 + 41^2 = 1706
-> 1^2 + 7^2 + 0^2 + 6^2 = 86
-> 8^2 + 6^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
72 [length 6]
-> 72^2 = 5184
-> 51^2 + 8^2 + 4^2 = 2681
-> 2681^2 = 7187761
-> 7^2 + 1^2 + 8^2 + 77^2 + 6^2 + 1^2 = 6080
-> 6^2 + 0^2 + 8^2 + 0^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
73 [length 5]
-> 73^2 = 5329
-> 5^2 + 32^2 + 9^2 = 1130
-> 11^2 + 3^2 + 0^2 = 130
-> 1^2 + 3^2 + 0^2 = 10
-> 1^2 + 0^2 = 1
74 [length 4]
-> 74^2 = 5476
-> 54^2 + 7^2 + 6^2 = 3001
-> 3^2 + 0^2 + 0^2 + 1^2 = 10
-> 1^2 + 0^2 = 1
75 [length 5]
-> 7^2 + 5^2 = 74
-> 74^2 = 5476
-> 54^2 + 7^2 + 6^2 = 3001
-> 3^2 + 0^2 + 0^2 + 1^2 = 10
-> 1^2 + 0^2 = 1
76 [length 5]
-> 76^2 = 5776
-> 5776^2 = 33362176
-> 33^2 + 362^2 + 1^2 + 7^2 + 6^2 = 132219
-> 1^2 + 3^2 + 2^2 + 2^2 + 1^2 + 9^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
77 [length 4]
-> 77^2 = 5929
-> 592^2 + 9^2 = 350545
-> 3^2 + 5^2 + 0^2 + 5^2 + 4^2 + 5^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
78 [length 4]
-> 7^2 + 8^2 = 113
-> 11^2 + 3^2 = 130
-> 1^2 + 3^2 + 0^2 = 10
-> 1^2 + 0^2 = 1
79 [length 3]
-> 7^2 + 9^2 = 130
-> 1^2 + 3^2 + 0^2 = 10
-> 1^2 + 0^2 = 1
80 [length 5]
-> 8^2 + 0^2 = 64
-> 64^2 = 4096
-> 40^2 + 9^2 + 6^2 = 1717
-> 1^2 + 7^2 + 1^2 + 7^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
81 [length 5]
-> 81^2 = 6561
-> 6^2 + 56^2 + 1^2 = 3173
-> 3^2 + 1^2 + 7^2 + 3^2 = 68
-> 6^2 + 8^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
82 [length 3]
-> 8^2 + 2^2 = 68
-> 6^2 + 8^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
83 [length 5]
-> 83^2 = 6889
-> 688^2 + 9^2 = 473425
-> 4734^2 + 25^2 = 22411381
-> 2^2 + 2^2 + 4^2 + 1^2 + 1^2 + 3^2 + 8^2 + 1^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
84 [length 5]
-> 84^2 = 7056
-> 7^2 + 0^2 + 56^2 = 3185
-> 318^2 + 5^2 = 101149
-> 1^2 + 0^2 + 1^2 + 1^2 + 4^2 + 9^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
85 [length 5]
-> 85^2 = 7225
-> 7^2 + 2^2 + 2^2 + 5^2 = 82
-> 8^2 + 2^2 = 68
-> 6^2 + 8^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
86 [length 2]
-> 8^2 + 6^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
87 [length 4]
-> 8^2 + 7^2 = 113
-> 11^2 + 3^2 = 130
-> 1^2 + 3^2 + 0^2 = 10
-> 1^2 + 0^2 = 1
88 [length 4]
-> 88^2 = 7744
-> 7^2 + 7^2 + 4^2 + 4^2 = 130
-> 1^2 + 3^2 + 0^2 = 10
-> 1^2 + 0^2 = 1
89 [length 5]
-> 8^2 + 9^2 = 145
-> 1^2 + 45^2 = 2026
-> 2^2 + 0^2 + 26^2 = 680
-> 6^2 + 8^2 + 0^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
90 [length 5]
-> 90^2 = 8100
-> 810^2 + 0^2 = 656100
-> 6^2 + 5^2 + 610^2 + 0^2 = 372161
-> 3^2 + 7^2 + 2^2 + 1^2 + 6^2 + 1^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
91 [length 4]
-> 9^2 + 1^2 = 82
-> 8^2 + 2^2 = 68
-> 6^2 + 8^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
92 [length 5]
-> 92^2 = 8464
-> 8464^2 = 71639296
-> 7^2 + 1^2 + 6^2 + 39^2 + 29^2 + 6^2 = 2484
-> 2^2 + 4^2 + 8^2 + 4^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
93 [length 5]
-> 93^2 = 8649
-> 8^2 + 649^2 = 421265
-> 4^2 + 2^2 + 1^2 + 2^2 + 6^2 + 5^2 = 86
-> 8^2 + 6^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
94 [length 4]
-> 9^2 + 4^2 = 97
-> 9^2 + 7^2 = 130
-> 1^2 + 3^2 + 0^2 = 10
-> 1^2 + 0^2 = 1
95 [length 5]
-> 95^2 = 9025
-> 9025^2 = 81450625
-> 81^2 + 4^2 + 506^2 + 2^2 + 5^2 = 262642
-> 2^2 + 6^2 + 2^2 + 6^2 + 4^2 + 2^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
96 [length 5]
-> 9^2 + 6^2 = 117
-> 117^2 = 13689
-> 13689^2 = 187388721
-> 18^2 + 7^2 + 3^2 + 8^2 + 8^2 + 7^2 + 21^2 = 1000
-> 1^2 + 0^2 + 0^2 + 0^2 = 1
97 [length 3]
-> 9^2 + 7^2 = 130
-> 1^2 + 3^2 + 0^2 = 10
-> 1^2 + 0^2 = 1
98 [length 5]
-> 9^2 + 8^2 = 145
-> 1^2 + 45^2 = 2026
-> 2^2 + 0^2 + 26^2 = 680
-> 6^2 + 8^2 + 0^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
99 [length 5]
-> 99^2 = 9801
-> 9^2 + 801^2 = 641682
-> 6416^2 + 8^2 + 2^2 = 41165124
-> 4^2 + 1^2 + 1^2 + 6^2 + 5^2 + 1^2 + 2^2 + 4^2 = 100
-> 1^2 + 0^2 + 0^2 = 1
100 [length 1]
-> 1^2 + 0^2 + 0^2 = 1
Friday, September 20, 2024
Friday, September 13, 2024
Recycling
One of the pastimes of living where we live is to curtain twitch a credible comprehension of human behaviour, such as it is.
Thursday, September 05, 2024
Unknown Havermann
I ran into my older sister's genealogy post on an Unknown Havermann yesterday and I was wondering how it ever came to this. Back in 2010 we had a brief email discussion on the matter (I've made some of my reply-text bold for emphasis):
16 Nov 2010
I read with interest your blog on our family tree. I am amazed that you were able to go back that far. Question: Generation V: Heinrich (living with his mother in 1900) +
[The Generation-V link is a 2022-updated page. The + is a date-of-death marker. In 2010, I did not yet know that date. I have a Neheim1900 excerpt that lists only some family names.]
I have a Heinrich who was a child of Sette – born: Jan.30/1901; died: Feb.26/1922 which seems to be at odds with your information that he was a child of Heinrich Havermann and Maria Messelke. Perhaps we are talking about another Heinrich?
17 Nov 2010 reply
My Heinrich came directly from dad's Stammbuch. I had scanned a copy of it for my computer but I have since lost that file because of a hard drive failure a couple of years ago. You will have to look at the original (assuming it wasn't thrown out). The residents-living-in-Neheim-in-1900 list basically confirms the existence of that person. He is old enough to be a Fabrikarbeiter and indeed, because his father died in 1876, he would have been at least 24 years old then.
18 Nov 2010
Thanks for your email clarifying my inquiry. I do have the "Ahnenpass". This seems to be a booklet that belonged to the relatives in Wattenscheid. Is this the same as the "Stammbuch" that you are referring to. I am willing to share the information with you if you want. Let me know.
18 Nov 2010 reply
[to part 1] Yes, that sounds like it. It does have Heinrich as a son of Heinrich, does it not?
[to part 2] No. I have all the information I need.
On my end, Heinrich wasn't an "unknown" (birthdate "estimated between 1844 and 1900"). He was Heinrich Anton, born 30 Jan 1876, three days before his father's death! Is it any wonder that his mother named him after his father? He died 26 Feb 1922. I don't know if he ever married or had children, but my sister listed a son, Heinrich (30 Jan 1901 - 26 Feb 1922), which perversely mirrors the actual Heinrich's particulars except for the year of birth. My sister suggested that Heinrich might have been a child of Sette but that would have made him a Rademacher, not a Havermann (an actual Heinrich Rademacher was 1907-1945).
I'm having difficulty finding a lot of my original sources for all this. Heinrich Anton's birth year of 1876 is in the Stadt- und Landständearchiv im Kloster Wedinghausen (Alphabetisches Register, 1874 - 1879). I'm pretty sure that I had found a reference to his Helden Friedhof burial in a book that corroborates his birth year but I've been unable to re-discover it.
Anyways, I just wanted this on the record in case some future researcher is confused by the geni.com misinformation. As mentioned in a previous blog, I have an extended Havermann family text chart and, as well, a slightly more limited pictorial chart. But beware. The "chesswanks" links are files on my computer and will likely disappear after my death.
Sunday, September 01, 2024
Goodbye Netflix, hello YouTube Premium
Today is the last day of my long-time (since April 2013) Netflix subscription and the first day of my new YouTube Premium subscription for which I'll be paying $3.95 less per month after my one-month-free trial.
Thursday, August 29, 2024
The pore structure of Clostridium perfringens epsilon toxin
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| [article] BioMoleculePlot3D (ribbons) in Wolfram 14.1: click to enlarge |
Friday, August 09, 2024
Alphabetizing the integers
Last month I wrote an article called "Integers, in alphabetical order" that illustrated my then-obsession with the topic. In February 1981, Ross Eckler had an article called "Alphabetizing the integers" (in the magazine Word Ways) that loosely anticipated my exploration.
On page 20 of his article, Eckler notes Philip Cohen's approach to the "Bergerson" problem (find the fixed points for integers 1 to n):
one one one four five five five eight eight
two three one four four four five five
two three one one one four four
two three six seven one nine
two three six seven one
two three six seven
two three six
two three
two
The number of fixed-point counts leads us to OEIS sequence A340671, which provides the actual fixed points in one of the links. Eckler gives us the list-sizes which produce matches for the first twenty integers. I have extended this listing to 100000 integers here. Eckler then notes that 3 appears (I am paraphrasing) in A340671 at positions 13 and 31 and asks for additional values. The third occurrence is at position 201 (then 203, 204, 208, ...). He didn't ask for a first 4, 5, 6, ... appearance as these were clearly beyond his realm of realizability at the time. But here they are:
1 1
2 2
3 13
4 202
5 213
6 2202
7 2213
8 14475
9 233164
10 320200
11 449694
12 2450694
13 4367488
14 4580804
15 4580824
The listing is for the first appearance of 1 to 15, giving the position/index at which it occurs. Michael Branicky found #12 on July 7. I determined #13 to #15 yesterday. The fixed points are added here.
Tuesday, July 30, 2024
Fun with digital roots
Éric Angelini's most recent blog is here. I was sufficiently intrigued with his challenge to find larger primes than his 20248751248751248751248751248751248751248751248751 that I gave it a go:
z(41) = 20 grows into z(89), Éric's 50-digit prime.
z(91) = 22 grows into z(280), a 191-digit prime.
z(300) = 35 grows into z(1064), a 766-digit prime.
z(3740) = 238 grows into z(d+3737), a d-digit (>150000) prime.
Up to this point, we have 151 primes in Z. Their positions/indices are: 2, 3, 4, 20, 21, 23, 26, 29, 31, 34, 37, 38, 40, 89, 280, 281, 284, 287, 290, 291, 293, 296, 299, 1064, 1066, 1073, 1078, 1079, 1081, 1084, 1085, 1144, 1147, 1170, 1171, 1184, 1221, 1262, 1263, 1265, 1268, 1271, 1278, 1280, 1287, 1616, 1617, 1619, 1660, 1665, 1698, 1700, 1703, 1706, 1707, 1712, 1719, 1721, 1724, 1729, 1784, 1787, 1789, 1792, 1897, 1899, 1914, 1919, 1920, 1922, 1965, 1972, 1973, 1978, 1983, 1986, 1993, 1998, 2001, 2022, 2043, 2045, 2064, 2075, 2076, 2097, 2100, 2103, 2104, 2106, 2109, 2112, 2115, 2225, 2242, 2243, 2245, 2248, 2293, 2336, 2338, 2363, 2366, 2369, 2371, 2388, 2393, 2396, 2513, 2516, 2517, 2660, 2693, 2696, 2697, 2699, 2704, 2709, 2724, 2727, 2744, 2747, 2748, 2750, 2795, 2800, 2801, 2803, 2810, 3156, 3183, 3188, 3191, 3204, 3206, 3225, 3290, 3293, 3360, 3427, 3462, 3475, 3477, 3484, 3485, 3487, 3506, 3511, 3512, 3515, 3738. So we are looking for prime #152 (the next one). I've put an indexed file of Z (to 3752) here.
One might suppose that in the absence of a definite d, we cannot continue Z. Actually, assuming that d exists, we can. What we cannot do is assign indices to the continuation, unless one is ok with:
d+3738 239 (prime #153)
d+3739 240
d+3740 241 (prime #154)
d+3741 242
d+3742 2428
d+3743 24287
...
I've computed 11288 terms of this continuation but, in order to make the file size smaller, I have removed d+7693 to d+15024 from view. The file is here. The final term at the bottom (index d+15025) is prime #190, a 7348-digit prime.
Festival!
The 1967 Murray Lerner documentary using Newport Folk Festivals (1963-1966) footage was on Turner Classic Movies recently and Catherine engaged me last Saturday about some issues. Mostly who some of the artists were. That's because TCM played the damned thing without subtitles, which is egregious.
Antti Alanen's 2017 blog post was a big help for its ordered listing but, as I watched the film myself, I realized that there were a number of deficiencies that were not being helped by simply Googling the Net. Eventually I looked for an .srt file for the movie and, upon finding one, realized that even though the text was crap, I could edit it to make it more presentable. Meaning that I couldn't actually see the subtitles on a copy of film, so I just organized it in a manner where a printed copy would be a decent adjunct for anyone watching an unsubtitled version of Festival.
00:00:37.121 --> 00:00:41.334 Jim Kweskin & the Jug Band: "Hannah Won't You Open That Door"
00:01:52.405 --> 00:01:54.865 Mel Lyman
00:02:25.896 --> 00:02:28.232 Jim Kweskin
00:02:38.034 --> 00:02:40.619 Fritz Richmond
00:03:36.133 --> 00:03:40.304 Joe Patterson: untitled quill instrumental
00:06:41.819 --> 00:06:46.198 Peter, Paul and Mary: "Come and Go With Me"
00:08:21.669 --> 00:08:25.005 voice of Peter Yarrow
00:08:51.281 --> 00:08:54.326 Peter, Paul and Mary: "If I Had a Hammer"
00:11:01.370 --> 00:11:05.165 The Sacred Harp Singers: "Rocky Road"
00:11:12.297 --> 00:11:15.300 voice of Pete Seeger
00:12:11.481 --> 00:12:15.485 The Georgia Sea Island Singers & Friends
00:12:15.569 --> 00:12:18.572 "Since I Lay My Burden Down"
00:13:00.739 --> 00:13:04.201 The Blue Ridge Mountain Dancers: clog dance
00:13:04.284 --> 00:13:08.789 accompanied by Pappy Clayton McMichen, Mike Seeger, Pete Seeger
00:15:24.341 --> 00:15:27.761 voice of Pete Seeger
00:15:36.853 --> 00:15:41.525 Tex Logan & The Lilly Brothers: "Black Mountain Rag"
00:15:46.780 --> 00:15:49.032 Taj Mahal
00:16:34.327 --> 00:16:37.998 Tex Logan & The Lilly Brothers
00:17:13.742 --> 00:17:16.369 "Green Corn"
00:17:16.453 --> 00:17:19.623 Pete Seeger, with Mel Lyman & Jim Kweskin
00:18:31.152 --> 00:18:34.572 voice of Tom Paxton
00:18:51.965 --> 00:18:55.969 Buffy St. Marie: "Cod'ine"
00:21:41.301 --> 00:21:45.638 Spider John Koerner: "Crazy Fool"
00:22:08.411 --> 00:22:12.123 Pete Seeger: "Deep Blue Sea"
00:22:33.937 --> 00:22:37.982 Odetta: "Carry It Back to Rosie"
00:23:25.446 --> 00:23:29.659 Joan Baez & Peter Yarrow: "Go Tell Aunt Rhody"
00:25:25.358 --> 00:25:29.112 voice of Peter Yarrow
00:25:59.559 --> 00:26:02.979 Joan Baez: "Mary Hamilton"
00:28:26.789 --> 00:28:30.751 voice of Ronnie Gilbert
00:29:39.820 --> 00:29:43.282 voice of Peter Yarrow
Bob Dylan: "Mr. Tambourine Man"
00:29:51.791 --> 00:29:55.461 Bob Dylan: "All I Really Want to Do"
Joan Baez: "From Me to You"
00:36:46.163 --> 00:36:49.875 Joan Baez: "All My Trials"
00:38:02.197 --> 00:38:05.742 Peter, Paul and Mary: "Blowin’ in The Wind"
00:39:49.221 --> 00:39:53.642 Donovan: "And The War Drags On"
00:40:36.143 --> 00:40:39.980 Judy Collins: ”Turn, Turn, Turn”
00:41:21.188 --> 00:41:24.483 Fiddler Beers
00:42:04.064 --> 00:42:07.776 Donovan: "Ballad of a Crystal Man"
00:42:59.536 --> 00:43:03.498 Odetta: "I Be's Troubled"
00:44:01.681 --> 00:44:05.685 Peter, Paul and Mary: "The Times They Are A’Changing"
00:46:29.079 --> 00:46:33.333 Joan Baez & Donovan: "Colours"
00:49:39.602 --> 00:49:43.857 Fred McDowell: "61 Highway Blues"
00:50:28.401 --> 00:50:31.321 Fred McDowell
00:51:15.531 --> 00:51:19.702 Sonny Terry & Brownie McGhee: "Key to The Highway"
00:52:24.809 --> 00:52:28.104 voice of Mississippi John Hurt
00:52:43.661 --> 00:52:46.664 Mississippi John Hurt: "Candy Man"
00:53:42.720 --> 00:53:47.683 Bob Dylan rehearsing with The Paul Butterfield Blues Band
00:53:50.645 --> 00:53:53.481 Almeda Riddle
00:54:35.648 --> 00:54:38.234 Joe Patterson
00:54:48.870 --> 00:54:51.747 Eck Robertson
00:54:59.714 --> 00:55:03.468 Mrs. General Watson and Mrs. Ollie Gilbert
00:55:42.465 --> 00:55:46.636 Horton Barker: "Pretty Sally"
00:56:50.575 --> 00:56:54.537 Bob Dylan & The Paul Butterfield Blues Band*: "Maggie's Farm"
00:59:30.735 --> 00:59:33.612 Mike Bloomfield
01:00:14.987 --> 01:00:19.408 Lonnie & Ed Young Fife & Drums Corps: instrumental
01:01:53.127 --> 01:01:55.963 The Swan Silvertones: "Feed Me Jesus"
01:02:29.163 --> 01:02:32.958 The Staple Singers: ”Help Me Jesus”
01:03:19.254 --> 01:03:21.715 The Freedom Singers
01:03:21.799 --> 01:03:25.928 "Up Above My Head I Hear Music in the Air"
01:04:05.759 --> 01:04:09.471 voice of professor Willis James
01:04:39.668 --> 01:04:43.547 The Freedom Singers: "Ain’t Gonna Let Nobody Turn Me Round"
01:05:15.079 --> 01:05:19.124 Fannie Lou Hamer & Company: "Go Tell It on The Mountain"
01:05:35.849 --> 01:05:39.728 voice of Pete Seeger
01:05:51.198 --> 01:05:54.368 The Freedom Singers: "All God's Children"
01:06:55.179 --> 01:06:58.724 "We Shall Overcome"
01:07:53.904 --> 01:07:57.032 The Paul Butterfield Blues Band: "Born in Chicago"
01:09:10.981 --> 01:09:13.608 Mike Bloomfield
01:09:42.929 --> 01:09:45.932 Son House
01:11:44.050 --> 01:11:47.846 Son House: "Downhearted Blues"
01:13:37.163 --> 01:13:39.833 "Levee Camp Moan"
The Paul Butterfield Blues Band: instrumental
01:16:48.521 --> 01:16:52.358 Howlin' Wolf: "Howlin' for My Darling"
01:19:20.924 --> 01:19:25.386 Mimi & Richard Fariña: "Reno Nevada"
01:20:30.702 --> 01:20:34.706 "Pack Up Your Sorrows"
01:21:12.869 --> 01:21:15.621 Mel Lyman
01:21:27.508 --> 01:21:30.344 Spokes Mashiyane: flute instrumental
01:22:24.315 --> 01:22:28.277 Cousin Emmy: "Turkey in the Straw"
01:22:42.333 --> 01:22:45.336 Theodore Bikel: "Karabli"
01:23:36.137 --> 01:23:39.557 Judy Collins: "Anathea"
01:24:58.886 --> 01:25:03.224 Johnny Cash: "I Walk the Line"
01:25:48.728 --> 01:25:52.315 The Osborne Brothers: "Ruby"
01:27:34.375 --> 01:27:38.170 Joan Baez: "Farewell Angelina"
01:29:13.933 --> 01:29:17.728 Bob Dylan: "Mr. Tambourine Man"
01:31:33.947 --> 01:31:37.242 Peter, Paul and Mary
Paul Stookey: "On a Desert Island"
01:32:34.174 --> 01:32:37.386 "Rising of the Moon"
01:34:46.014 --> 01:34:49.268 Pete Seeger, et al., group finale: "Down by the Riverside"
* minus Paul Butterfield, plus Al Kooper & Barry Goldberg
Saturday, July 20, 2024
Winery
 |
| click to enlarge |
Emily (my daughter, taking the photo) is helping out in a (short documentary) movie shoot.
Wednesday, July 17, 2024
Power interruption
One could say that yesterday morning's rainfall was significant! At around 12:40 pm we lost power and, unlike to the usual once-a-week (or so) off-and-ons, this one lasted until 6:25 pm. Apart from having to rediscover some camping survival skills during the outage, restoring my ongoing Leyland prime searches on sixteen computers (once power was restored) took me to 10:30 pm. Unfortunately, seven days of an expected fifteen-day run calculating five million terms of the Philip Cohen sequence is lost.
Monday, July 15, 2024
Khinchin geometric means
I first did a geometric-means analysis for Khinchin's constant (K) in early 2000 using 110000 decimal digits of the number. Late Friday, Neil Sloane informed me that a Carlos Simó had calculated one million digits! Converting these to 969680 continued-fraction terms, I did a reanalysis:
.png) |
| click to enlarge |
In this range, the final time that the mean changes sign is from (540114, -9.67033*10^-7) to (540115, 0.0000323051). The record (proximity to K) mean at 353014 is -4.14662*10^-9.
Thursday, July 11, 2024
Integers, in alphabetical order
I have been preoccupied, since the beginning of July, about integers in alphabetical order. Claudio Meller wrote this preamble to the Sequence Fanatics discussion list (taken from a British game show called The 1% Club): "If all the numbers from 1 to 20 are written out in words and put into numerical order and then reorganised into alphabetical order, which is the only number that stays in the same position?" Claudio had noticed that, replacing 20 with other integers up to 1000, "all the numbers up to 399 are kept in their position at least once". I replied: "Not 8 or 18". Well, Claudio was wrong about 8 but I was wrong about 18. Claudio pointed out that 18 shows up for 1 to 815.
It hadn't shown up for 1 to 815 for me because I was using a letter-by-letter alphabetical order (spaces and punctuation are ignored) while Claudio was using a word-by-word alphabetical order (spaces are not ignored, a space preceding any letter of the alphabet).
In a Wikipedia article on alphabetical order, the treatment of multi-word strings reiterates again the two-fold situation: word-by-word or letter-by-letter. What's new to me is that the latter may sometimes be called "dictionary order".
Mathematica has an AlphabeticSort function that appears to function word-by-word. I am going to assume that word-by-word is the alphabetical-order prevailing standard and, if anyone prefers letter-by-letter, they ought to spell it out.
We are looking for the start of the integers in alphabetical order (American English, by which we mean Mathematica's IntegerName[#,"Words"]). I will point out that IntegerName uses a non-standard hyphen (character code 8208) instead of the normal, generic hyphen (character code 45). I'll never understand why they did that, but I digress.
In American English all integer names start with one of e, f, n, o, s, or t, so the first term is necessarily "eight". Since we are working in alphabetical order (i.e., word-by-word), the next term should incorporate an additional word. Mathematica has integer names up to (but not including) 10^306 and the alphabetically first word that fits is "billion", so "eight billion" is our second term. As before, we are looking for an additional word that will turn "eight billion" into a new integer. Our third term will be "eight billion eight". Our fourth term will be "eight billion eight hundred".
I decided to Google my four terms and got one hit (the reason I didn't link to the hit is because the webpage doesn't have the Google snippet information on it):
For some reason somebody thought "eight billion eight million" was the fifth term, followed by "eight billion eight thousand", "eight billion eighteen". In my mind, extending the sequence with additional words is the way to proceed. If an additional word is not logically possible, then we consider replacing the final existing word:
eight
eight billion
eight billion eight
eight billion eight hundred
eight billion eight hundred eight
eight billion eight hundred eight million
eight billion eight hundred eight million eight
eight billion eight hundred eight million eight hundred
eight billion eight hundred eight million eight hundred eight
eight billion eight hundred eight million eight hundred eight thousand
eight billion eight hundred eight million eight hundred eight thousand eight
eight billion eight hundred eight million eight hundred eight thousand eight hundred
eight billion eight hundred eight million eight hundred eight thousand eight hundred eight
eight billion eight hundred eight million eight hundred eight thousand eight hundred eighteen
eight billion eight hundred eight million eight hundred eight thousand eight hundred eighty
eight billion eight hundred eight million eight hundred eight thousand eight hundred eighty-eight
eight billion eight hundred eight million eight hundred eight thousand eight hundred eighty-five
eight billion eight hundred eight million eight hundred eight thousand eight hundred eighty-four
eight billion eight hundred eight million eight hundred eight thousand eight hundred eighty-nine
eight billion eight hundred eight million eight hundred eight thousand eight hundred eighty-one
eight billion eight hundred eight million eight hundred eight thousand eight hundred eighty-seven
eight billion eight hundred eight million eight hundred eight thousand eight hundred eighty-six
eight billion eight hundred eight million eight hundred eight thousand eight hundred eighty-three
eight billion eight hundred eight million eight hundred eight thousand eight hundred eighty-two
eight billion eight hundred eight million eight hundred eight thousand eight hundred eleven
eight billion eight hundred eight million eight hundred eight thousand eight hundred fifteen
eight billion eight hundred eight million eight hundred eight thousand eight hundred fifty
eight billion eight hundred eight million eight hundred eight thousand eight hundred fifty-eight
eight billion eight hundred eight million eight hundred eight thousand eight hundred fifty-five
eight billion eight hundred eight million eight hundred eight thousand eight hundred fifty-four
eight billion eight hundred eight million eight hundred eight thousand eight hundred fifty-nine
eight billion eight hundred eight million eight hundred eight thousand eight hundred fifty-one
eight billion eight hundred eight million eight hundred eight thousand eight hundred fifty-seven
eight billion eight hundred eight million eight hundred eight thousand eight hundred fifty-six
eight billion eight hundred eight million eight hundred eight thousand eight hundred fifty-three
eight billion eight hundred eight million eight hundred eight thousand eight hundred fifty-two
eight billion eight hundred eight million eight hundred eight thousand eight hundred five
eight billion eight hundred eight million eight hundred eight thousand eight hundred forty
eight billion eight hundred eight million eight hundred eight thousand eight hundred forty-eight
eight billion eight hundred eight million eight hundred eight thousand eight hundred forty-five
eight billion eight hundred eight million eight hundred eight thousand eight hundred forty-four
eight billion eight hundred eight million eight hundred eight thousand eight hundred forty-nine
eight billion eight hundred eight million eight hundred eight thousand eight hundred forty-one
eight billion eight hundred eight million eight hundred eight thousand eight hundred forty-seven
eight billion eight hundred eight million eight hundred eight thousand eight hundred forty-six
eight billion eight hundred eight million eight hundred eight thousand eight hundred forty-three
eight billion eight hundred eight million eight hundred eight thousand eight hundred forty-two
eight billion eight hundred eight million eight hundred eight thousand eight hundred four
eight billion eight hundred eight million eight hundred eight thousand eight hundred fourteen
eight billion eight hundred eight million eight hundred eight thousand eight hundred nine
eight billion eight hundred eight million eight hundred eight thousand eight hundred nineteen
eight billion eight hundred eight million eight hundred eight thousand eight hundred ninety
eight billion eight hundred eight million eight hundred eight thousand eight hundred ninety-eight
eight billion eight hundred eight million eight hundred eight thousand eight hundred ninety-five
eight billion eight hundred eight million eight hundred eight thousand eight hundred ninety-four
eight billion eight hundred eight million eight hundred eight thousand eight hundred ninety-nine
eight billion eight hundred eight million eight hundred eight thousand eight hundred ninety-one
eight billion eight hundred eight million eight hundred eight thousand eight hundred ninety-seven
eight billion eight hundred eight million eight hundred eight thousand eight hundred ninety-six
eight billion eight hundred eight million eight hundred eight thousand eight hundred ninety-three
eight billion eight hundred eight million eight hundred eight thousand eight hundred ninety-two
eight billion eight hundred eight million eight hundred eight thousand eight hundred one
eight billion eight hundred eight million eight hundred eight thousand eight hundred seven
eight billion eight hundred eight million eight hundred eight thousand eight hundred seventeen
eight billion eight hundred eight million eight hundred eight thousand eight hundred seventy
eight billion eight hundred eight million eight hundred eight thousand eight hundred seventy-eight
eight billion eight hundred eight million eight hundred eight thousand eight hundred seventy-five
eight billion eight hundred eight million eight hundred eight thousand eight hundred seventy-four
eight billion eight hundred eight million eight hundred eight thousand eight hundred seventy-nine
eight billion eight hundred eight million eight hundred eight thousand eight hundred seventy-one
eight billion eight hundred eight million eight hundred eight thousand eight hundred seventy-seven
eight billion eight hundred eight million eight hundred eight thousand eight hundred seventy-six
eight billion eight hundred eight million eight hundred eight thousand eight hundred seventy-three
eight billion eight hundred eight million eight hundred eight thousand eight hundred seventy-two
eight billion eight hundred eight million eight hundred eight thousand eight hundred six
eight billion eight hundred eight million eight hundred eight thousand eight hundred sixteen
eight billion eight hundred eight million eight hundred eight thousand eight hundred sixty
eight billion eight hundred eight million eight hundred eight thousand eight hundred sixty-eight
eight billion eight hundred eight million eight hundred eight thousand eight hundred sixty-five
eight billion eight hundred eight million eight hundred eight thousand eight hundred sixty-four
eight billion eight hundred eight million eight hundred eight thousand eight hundred sixty-nine
eight billion eight hundred eight million eight hundred eight thousand eight hundred sixty-one
eight billion eight hundred eight million eight hundred eight thousand eight hundred sixty-seven
eight billion eight hundred eight million eight hundred eight thousand eight hundred sixty-six
eight billion eight hundred eight million eight hundred eight thousand eight hundred sixty-three
eight billion eight hundred eight million eight hundred eight thousand eight hundred sixty-two
eight billion eight hundred eight million eight hundred eight thousand eight hundred ten
eight billion eight hundred eight million eight hundred eight thousand eight hundred thirteen
eight billion eight hundred eight million eight hundred eight thousand eight hundred thirty
eight billion eight hundred eight million eight hundred eight thousand eight hundred thirty-eight
eight billion eight hundred eight million eight hundred eight thousand eight hundred thirty-five
eight billion eight hundred eight million eight hundred eight thousand eight hundred thirty-four
eight billion eight hundred eight million eight hundred eight thousand eight hundred thirty-nine
eight billion eight hundred eight million eight hundred eight thousand eight hundred thirty-one
eight billion eight hundred eight million eight hundred eight thousand eight hundred thirty-seven
eight billion eight hundred eight million eight hundred eight thousand eight hundred thirty-six
eight billion eight hundred eight million eight hundred eight thousand eight hundred thirty-three
eight billion eight hundred eight million eight hundred eight thousand eight hundred thirty-two
eight billion eight hundred eight million eight hundred eight thousand eight hundred three
eight billion eight hundred eight million eight hundred eight thousand eight hundred twelve
eight billion eight hundred eight million eight hundred eight thousand eight hundred twenty
eight billion eight hundred eight million eight hundred eight thousand eight hundred twenty-eight
eight billion eight hundred eight million eight hundred eight thousand eight hundred twenty-five
eight billion eight hundred eight million eight hundred eight thousand eight hundred twenty-four
eight billion eight hundred eight million eight hundred eight thousand eight hundred twenty-nine
eight billion eight hundred eight million eight hundred eight thousand eight hundred twenty-one
eight billion eight hundred eight million eight hundred eight thousand eight hundred twenty-seven
eight billion eight hundred eight million eight hundred eight thousand eight hundred twenty-six
eight billion eight hundred eight million eight hundred eight thousand eight hundred twenty-three
eight billion eight hundred eight million eight hundred eight thousand eight hundred twenty-two
eight billion eight hundred eight million eight hundred eight thousand eight hundred two
eight billion eight hundred eight million eight hundred eight thousand eighteen
eight billion eight hundred eight million eight hundred eight thousand eighty
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...
* A couple of two-consecutive primes are shown. The first three-consecutive primes instance:
eight billion eight hundred eight million eight hundred eighteen thousand five hundred sixty-nine
eight billion eight hundred eight million eight hundred eighteen thousand five hundred sixty-one
eight billion eight hundred eight million eight hundred eighteen thousand five hundred sixty-one
eight billion eight hundred eight million eight hundred eighteen thousand five hundred sixty-seven
Subscribe to:
Posts (Atom)