Tuesday, February 5

Engineering 101

The year-ago ice jam hit the Raymore Park construction site hard. The area was the west-side-of-the-river staging point for an under-the-river pipe-refitting project.


A few months later things seemed back to normal. There were a couple of dirt mounds adjacent to the manhole entrance.


In light of the recurring ice jams on the river, an engineering student might have thought to distribute the dirt in situ so as to level the top of the manhole with the surrounding ground. But there were no such engineering students on hand, so they decided to haul the dirt away.


In late-September, early-October, a thin layer of soil — likely with embedded grass seed — was added to the site.


Here is how the manhole entrance appeared on October 16:


Here is how it appeared this morning after the current warm-spell ice melt:


I'm wondering if the top concrete layer has been sheared off.

February 8 update:

Monday, January 28

Pseudo-binary ænlic primes

I discussed ænlic primes here. By pseudo-binary I mean decimal numbers that contain only digits zero and one. I will cover here three types of pseudo-binary ænlic primes:

1. Repunit primes. These are terms of A004022. They are ænlic primes by default — no other permutation of their digits is prime (because no other permutation of their digits exists). The repunit number (10^a-1)/9 is an ænlic prime for a = 2, 19, 23, 317, 1031, 49081, 86453, 109297, 270343, ...

2. Primes composed of all ones except for one zero. The number (10^a-1)/9-10^b is an ænlic prime for (a,b) = (5,3), (6,4), (9,7), (26,13), (29,5), (33,13), (35,7), (39,23), (51,43), (53,37), (56,8), (74,44), (77,33), (80,11), (83,31), (89,39), (90,83), (92,53), (105,67), (107,11), (108,99), (110,61), (113,73), (126,44), (129,109), (134,80), (147,19), (149,15), (153,25), (164,15), (170,6), (174,62), (176,113), (177,167), (182,17), (185,37), (192,80), (194,26), (195,151), (201,53), (204,131), (215,119), (219,167), (221,181), (225,211), (227,223), (228,215), (230,32), (231,127), (234,208), (236,207), (246,76), (249,23), (251,147), (260,235), (263,151), (267,43), (270,128), (284,199), (285,53), (288,54), (297,13), (305,269), (314,278), (315,227), (317,125), (321,101), (324,320), (329,135), (330,289), (348,3), (363,83), (369,125), (371,131), (381,127), (387,379), (389,95), (396,262), (417,287), (419,119), (443,55), (446,342), (450,209), (453,421), (461,289), (467,459), (473,213), (477,53), (480,242), (491,31), (492,124), (497,423), (503,439), (504,486), (506,446), (512,83), (518,131), (521,419), (525,289), (539,483), (540,8), (545,247), (546,128), (548,284), (566,361), (567,103), (572,492), (579,83), (582,160), (588,396), (593,135), (605,79), (606,521), (609,163), (611,363), (618,208), (629,89), (632,293), (635,311), (641,331), (650,123), (653,33), (656,363), (657,175), (659,535), (674,626), (677,655), (681,509), (692,132), (698,209), (708,347), (710,25), (711,623), (713,451), (720,120), (729,697), (750,146), (752,98), (765,167), (770,530), (779,355), (780,84), (791,623), (803,459), (804,148), (806,13), (809,105), (816,336), (828,816), (833,491), (836,399), (837,425), (845,35), (848,521), (849,691), (857,545), (858,627), (861,293), (870,112), (872,475), (875,771), (885,703), (890,87), (893,85), (897,487), (912,35), (914,168), (923,71), (935,415), (939,295), (945,169), (954,897), (956,746), (969,311), (984,695), (993,397), (1001,259), (1017,151), (1019,735), (1020,843), (1022,629), (1029,923), (1037,289), (1040,11), (1052,559), (1067,863), (1070,750), (1077,695), (1083,631), (1085,463), (1086,1073), (1091,511), (1095,655), (1097,565), (1101,997), (1110,626), (1112,889), (1124,561), (1127,711), (1136,737), (1139,999), (1140,310), (1146,526), (1148,119), (1149,253), (1155,455), (1160,746), (1161,61), (1163,227), (1173,187), (1175,983), (1184,347), (1196,557), (1199,623), (1202,194), (1203,583), (1208,189), (1217,35), (1230,1190), (1232,277), (1235,959), (1254,1035), (1256,1083), (1259,1143), (1265,735), (1274,1199), (1277,1113), (1287,607), (1289,755), (1302,446), (1307,1235), (1320,239), (1328,853), (1331,139), (1338,905), (1346,1237), (1353,907), (1361,1329), (1365,635), (1373,1269), (1376,608), (1377,83), (1382,547), (1385,545), (1392,638), (1407,383), (1409,245), (1421,377), (1433,1013), (1451,1239), (1466,999), (1470,1159), (1472,1344), (1473,271), (1481,1059), (1485,325), (1487,527), (1509,467), (1511,1231), (1514,1039), (1515,443), (1517,1239), (1521,229), (1523,947), (1526,529), (1529,421), (1532,1205), (1533,749), (1541,1123), (1548,1388), (1550,828), (1553,1351), (1554,684), (1556,746), (1566,738), (1568,1001), (1572,1244), (1586,843), (1589,1017), (1598,168), (1604,289), (1613,319), (1617,139), (1620,4), (1625,69), (1635,1595), (1641,841), (1643,427), (1658,1299), (1662,1486), (1665,479), (1670,1214), (1686,191), (1688,114), (1689,637), (1700,524), (1706,3), (1707,383), (1709,1607), (1716,83), (1721,369), (1725,223), (1731,119), (1737,941), (1739,1435), (1757,1491), (1763,1019), (1766,893), (1770,104), (1773,661), (1793,601), (1796,1003), (1797,421), (1802,380), (1805,229), (1809,13), (1811,23), (1815,719), (1818,1181), (1821,751), (1836,177), (1850,143), (1862,1407), (1880,294), (1904,1195), (1905,1891), (1907,1839), (1914,1012), (1926,1226), (1929,473), (1934,1017), (1955,303), (1956,416), (1958,1081), (1970,1755), (1973,331), (1985,1355), (1986,1426), (1992,1083), (1995,535), (2010,1518), (2016,396), (2019,683), (2021,1977), (2034,1186), (2036,476), (2037,1451), (2039,1679), (2040,1270), (2048,543), (2058,2022), (2060,752), (2063,1071), (2067,1895), (2069,2045), (2070,2001), (2084,1065), (2085,1865), (2091,491), (2094,25), (2097,1463), (2105,1011), (2112,41), (2115,1007), (2123,531), (2124,1345), (2127,2063), (2135,79), (2136,1214), (2138,62), (2141,57), (2147,1515), (2166,1426), (2178,1320), (2192,120), (2193,509), (2195,1723), (2198,1739), (2204,895), (2205,611), (2208,1648), (2210,1697), (2213,1523), (2217,593), (2219,1643), (2225,481), (2234,755), (2235,991), (2249,2123), (2255,1711), (2259,467), (2261,1909), (2262,13), (2264,2113), (2265,1351), (2289,823), (2306,1038), (2309,1305), (2316,594), (2321,553), (2324,1089), (2325,907), (2328,1015), (2336,1403), (2339,1703), (2345,665), (2354,901), (2366,1886), (2373,461), (2379,107), (2385,1225), (2387,159), (2388,1713), (2390,1353), (2394,152), (2397,1295), (2400,463), (2403,203), (2409,5), (2411,459), (2417,257), (2420,1700), (2426,1389), (2430,2106), (2432,857), (2433,751), (2439,2239), (2441,599), (2447,943), (2451,1543), (2457,1609), (2465,1339), (2472,1648), (2478,232), (2481,1781), (2486,1817), (2489,969), (2490,1304), (2498,1541), (2501,2117), (2508,864), (2513,673), (2519,1679), (2520,223), (2522,2466), (2526,1522), (2528,2067), (2535,1567), (2537,1889), (2546,108), (2549,757), (2550,1175), (2552,889), (2553,1933), (2561,863), (2564,2363), (2565,359), (2567,2039), (2571,839), (2574,1322), (2577,1129), (2585,967), (2594,313), (2595,607), (2597,2019), (2598,974), (2601,2329), (2606,1229), (2610,1192), (2612,1987), (2616,1281), (2618,1827), (2621,2607), (2628,1762), (2633,2073), (2636,903), (2646,1011), (2661,1321), (2670,810), (2673,2095), (2688,2672), (2693,1033), (2694,1187), (2696,2568), (2708,855), (2733,1537), (2759,1119), (2766,2361), (2769,383), (2774,558), (2784,1545), (2789,1019), (2793,2023), (2795,1863), (2796,2563), (2802,2724), (2804,1610), (2807,1455), (2816,449), (2822,356), (2826,1362), (2828,635), (2844,2126), (2846,2597), (2856,2573), (2858,593), (2861,1197), (2865,991), (2867,991), (2873,1801), (2877,1085), (2882,1454), (2883,779), (2885,1065), (2889,1579), (2897,2701), (2903,1031), (2904,894), (2912,165), (2925,197), (2927,447), (2931,1063), (2939,2755), (2948,727), (2954,2369), (2963,2711), (2966,1316), (2981,421), (2987,1155), (2993,555), (2996,608), (2997,2777), (3008,1807), (3009,2405), (3020,2891), (3027,823), (3033,361), (3041,1847), (3044,2694), (3047,1359), (3066,2488), (3075,3031), (3080,1537), (3081,817), (3083,2107), (3111,2519), (3114,12), (3116,848), (3126,1936), (3128,1927), (3129,343), (3131,2847), (3135,1663), (3137,2399), (3156,2089), (3165,2035), (3170,896), (3173,875), (3186,2354), (3191,1047), (3201,1219), (3209,2407), (3213,2951), (3233,2885), (3239,983), (3242,1188), (3246,1819), (3249,3173), (3255,3223), (3260,2767), (3263,1535), (3266,798), (3267,1699), (3282,1098), (3290,1988), (3296,2093), (3306,1708), (3311,3023), (3312,2481), (3315,919), (3320,1875), (3324,1342), (3332,2474), (3341,2493), (3348,1870), (3353,2917), (3356,739), (3357,871), (3365,1673), (3369,3059), (3381,2693), (3398,2421), (3399,2959), (3401,2247), (3410,193), (3422,427), (3426,2937), (3452,2364), (3459,1255), (3467,2375), (3477,3253), (3485,783), (3489,73), (3494,1003), (3506,2407), (3509,123), (3524,539), (3531,487), (3533,985), (3536,1847), (3537,847), (3539,1643), (3545,1243), (3561,593), (3564,3341), (3570,3482), (3578,149), (3587,1791), (3593,427), (3597,937), (3609,1105), (3614,887), (3615,1535), (3618,3464), (3629,3285), (3641,2459), (3648,2379), (3657,2615), (3666,3056), (3669,1045), (3677,3015), (3686,3103), (3689,3107), (3690,2692), (3698,401), (3699,2047), (3702,2292), (3704,2503), (3708,2718), (3714,1189), (3723,1343), (3725,783), (3734,3669), (3737,293), (3747,263), (3755,827), (3759,671), (3761,1019), (3777,2821), (3779,3011), (3782,2231), (3783,3335), (3785,821), (3791,799), (3794,63), (3795,2231), (3798,2092), (3812,1435), (3821,1769), (3825,1187), (3834,2088), (3837,1235), (3851,3271), (3855,607), (3858,66), (3864,3224), (3866,307), (3867,1255), (3872,1982), (3876,3329), (3881,2461), (3887,3791), (3888,1640), (3891,1799), (3896,3377), (3920,848), (3923,779), (3924,1629), (3927,1879), (3936,2181), (3939,1159), (3941,1811), (3942,3348), (3947,2307), (3968,2964), (3969,653), (3975,3223), (3980,926), (3989,3385), (3996,3846), (4004,3722), (4005,295), (4017,743), (4020,2780), (4046,2039), (4053,3251), (4058,3371), (4059,3151), (4061,2773), (4062,1576), (4064,1435), (4067,3243), (4068,590), (4073,2597), (4091,3883), (4097,567), (4100,2737), (4101,2483), (4106,947), (4113,2231), (4115,643), (4118,377), (4139,3319), (4142,2821), (4148,889), (4149,1909), (4154,1620), (4160,3499), (4169,1309), (4179,1063), (4184,3667), (4188,452), (4197,3167), (4200,1198), (4203,427), (4211,1939), (4214,1227), (4218,3115), (4221,503), (4226,318), (4229,1427), (4232,2198), (4235,695), (4238,3444), (4241,977), (4245,835), (4247,3679), (4256,551), (4257,2287), (4259,3195), (4262,1970), (4263,1775), (4265,1489), (4266,249), (4269,2543), (4275,779), (4277,4091), (4281,3961), (4289,2387), (4293,4085), (4298,1166), (4301,1021), (4304,4116), (4307,3347), (4316,2149), (4325,461), (4332,1277), (4334,1935), (4337,2585), (4353,911), (4355,2039), (4356,2452), (4358,753), (4359,2407), (4361,1049), (4365,433), (4368,3505), (4370,2113), (4376,863), (4377,2311), (4395,4339), (4400,987), (4401,2993), (4403,3651), (4409,1781), (4418,2735), (4424,276), (4433,4319), (4436,4003), (4437,377), (4449,3119), (4451,399), (4454,240), (4455,2527), (4460,2165), (4463,1167), (4478,2304), (4481,3209), (4484,3163), (4485,149), (4490,2162), (4493,3767), (4499,319), (4505,427), (4506,1404), (4517,587), (4521,4141), (4526,3689), (4535,351), (4538,2917), (4542,3615), (4547,1743), (4548,2601), (4553,439), (4556,3509), (4559,1839), (4560,1397), (4565,4149), (4568,651), (4569,1061), (4571,2687), (4578,1734), (4580,846), (4581,541), (4586,1976), (4589,2197), (4593,503), (4608,2017), (4617,203), (4619,1455), (4629,3797), (4638,1778), (4641,4327), (4643,2135), (4646,1638), (4649,3149), (4656,244), (4658,1813), (4686,1206), (4700,1007), (4703,2559), (4707,1399), (4709,1753), (4713,3883), (4725,3079), (4728,1648), (4730,3371), (4733,3719), (4736,339), (4739,3115), (4740,1004), (4745,555), (4746,2662), (4748,824), (4752,240), (4757,35), (4761,3671), (4769,2495), (4773,2183), (4776,3427), (4784,270), (4787,4495), (4793,217), (4796,239), (4802,3989), (4805,715), (4818,2755), (4820,1099), (4821,2351), (4826,1653), (4829,4721), (4833,3359), (4835,879), (4851,511), (4853,1319), (4854,4423), (4856,4477), (4878,1071), (4881,1373), (4883,739), (4884,748), (4886,327), (4898,3849), (4905,725), (4908,232), (4917,1399), (4919,3951), (4925,2659), (4929,4297), (4931,311), (4947,547), (4952,4455), (4955,831), (4958,1553), (4961,153), (4964,4205), (4977,3875), (4989,359), (5001,3403), (5006,2591), (5009,2893), (5018,3570), (5019,391), (5025,1025), (5027,783), (5030,3686), (5037,1261), (5045,3219), (5061,3523), (5063,527), (5064,1266), (5066,4099), (5073,989), (5076,402), (5084,3252), (5093,1239), (5096,2039), (5097,4675), (5099,1055), (5102,2082), (5108,4176), (5114,335), (5121,3103), (5123,2935), (5126,2802), (5135,1999), (5139,2803), (5148,4711), (5153,2893), (5159,4799), (5165,3333), (5168,4911), (5180,4565), (5186,3548), (5187,851), (5189,4755), (5193,4717), (5195,3739), (5201,2637), (5211,1687), (5219,1391), (5226,3709), (5229,3577), (5232,4567), (5235,1007), (5237,5051), (5243,3743), (5249,1401), (5250,179), (5252,1485), (5259,1775), (5262,267), (5265,4423), (5273,5255), (5276,3979), (5285,655), (5294,2927), (5298,4206), (5300,559), (5316,5302), (5331,1939), (5333,3187), (5337,5323), (5339,2411), (5345,3893), (5348,3908), (5351,4159), (5363,2551), (5373,205), (5381,2487), (5382,4234), (5384,4317), (5388,4150), (5399,3143), (5406,1736), (5408,4602), (5409,293), (5411,1979), (5421,5263), (5433,5203), (5438,2693), (5441,5171), (5445,4349), (5453,3793), (5457,5375), (5466,1436), (5468,167), (5474,4931), (5477,5285), (5481,3853), (5483,2603), (5487,367), (5489,4013), (5493,2501), (5496,3928), (5498,1819), (5505,3371), (5520,2747), (5526,3918), (5529,2483), (5531,3587), (5535,2911), (5544,4507), (5553,5411), (5561,563), (5565,2341), (5573,1501), (5576,2952), (5589,5047), (5619,623), (5622,2668), (5625,13), (5639,4959), (5651,2123), (5658,1435), (5660,5359), (5682,4722), (5694,758), (5697,1241), (5717,3561), (5720,3433), (5721,4327), (5726,3758), (5733,3277), (5741,717), (5747,263), (5750,1710), (5754,2301), (5756,5323), (5763,203), (5765,2733), (5769,4387), (5774,488), (5777,4469), (5781,5183), (5786,5459), (5795,4567), (5807,5567), (5816,5293), (5822,4983), (5826,2469), (5829,3895), (5837,2343), (5841,5839), (5843,31), (5847,2143), (5874,3064), (5892,5790), (5921,3513), (5925,2309), (5927,4679), (5928,5111), (5934,2729), (5936,3221), (5937,3047), (5943,5255), (5945,3645), (5948,5712), (5955,2423), (5957,5593), (5958,2628), (5963,795), (5964,1648), (5966,3183), (5969,4705), (5975,439), (5978,5111), (5981,3719), (5982,2593), (5987,947), (5991,3119), (5993,5625), (5996,728), (6000,5672), (6006,1988), (6017,821), (6018,421), (6023,4911), (6026,669), (6027,1567), (6032,5094), (6039,2879), (6041,251), (6048,1605), (6056,3167), (6066,2939), (6083,1155), (6092,5461), (6096,548), (6098,1831), (6101,3433), (6104,485), (6107,779), (6119,2159), (6126,1474), (6129,2177), (6131,1543), (6132,961), (6140,2279), (6141,3521), (6155,3267), (6164,884), (6173,4181), (6177,2921), (6186,2566), (6188,773), (6189,6119), (6194,409), (6200,3455), (6225,181), (6227,683), (6230,5977), (6234,338), (6236,1063), (6237,3955), (6239,1279), (6240,4833), (6242,1622), (6249,3115), (6266,2123), (6269,253), (6281,173), (6284,3582), (6299,5987), (6320,3469), (6324,2989), (6330,1691), (6350,2015), (6354,1427), (6359,1295), (6366,671), (6371,5127), (6372,3430), (6374,3857), (6375,2567), (6377,2893), (6383,319), (6389,3317), (6393,4663), (6395,5707), (6396,5848), (6402,4246), (6405,1427), (6407,6287), (6414,1080), (6416,3267), (6417,5273), (6420,5311), (6423,3823), (6429,6191), (6432,5852), (6434,5553), (6435,3239), (6437,4253), (6449,2083), (6452,1760), (6455,3055), (6459,1891), (6473,157), (6482,1452), (6486,2018), (6489,5305), (6500,4487), (6501,3589), (6506,2789), (6507,2171), (6513,5891), (6522,6289), (6525,6431), (6536,3417), (6546,3334), (6548,3091), (6557,1385), (6558,6404), (6570,5538), (6572,2161), (6581,6199), (6584,1013), (6585,5383), (6587,107), (6588,240), (6596,1089), (6605,1653), (6627,827), (6633,1747), (6635,415), (6651,1087), (6659,1743), (6660,105), (6675,607), (6689,6613), (6690,338), (6701,4249), (6707,2887), (6710,624), (6711,6143), (6714,3505), (6740,2568), (6741,2047), (6743,6503), (6749,6339), (6750,452), (6758,4621), (6759,4319), (6761,2979), (6762,881), (6764,2906), (6767,3823), (6785,5979), (6788,2600), (6821,4921), (6822,5648), (6825,2347), (6827,3583), (6828,1702), (6830,4495), (6831,3791), (6833,1791), (6836,5581), (6837,4441), (6846,1433), (6849,2935), (6852,746), (6860,4998), (6866,6699), (6867,5755), (6873,1867), (6876,549), (6887,6103), (6888,1856), (6893,1607), (6896,6092), (6932,6859), (6935,6183), (6936,6933), (6938,2425), (6950,2226), (6956,2679), (6974,4373), (6977,6947), (6978,3676), (6981,1789), (6989,2783), (6990,5726), (6999,2191), (7001,3729), (7005,4973), (7008,1268), (7010,4650), (7013,5461), (7014,1874), (7022,3512), (7028,3236), (7029,6775), (7043,531), (7049,1829), (7050,6471), (7053,2135), (7061,6047), (7068,145), (7077,5869), (7079,4879), (7080,4350), (7082,6325), (7085,5737), (7088,4958), (7092,2147), (7094,3489), (7098,1036), (7112,4171), (7115,3739), (7119,1391), (7136,1957), (7139,3823), (7145,2567), (7146,6039), (7152,6245), (7163,1047), (7169,1103), (7170,5173), (7173,6703), (7178,2785), (7179,1723), (7181,4003), (7185,3089), (7190,4442), (7193,4513), (7202,6959), (7206,2802), (7212,4390), (7217,2473), (7218,472), (7220,2180), (7224,2888), (7226,6823), (7227,6439), (7229,6423), (7232,143), (7235,1851), (7236,2682), (7241,1817), (7260,862), (7262,6869), (7272,1805), (7290,4459), (7296,5549), (7304,3072), (7307,3403), (7316,6569), (7323,2407), (7325,3513), (7326,6493), (7329,2485), (7343,3359), (7344,825), (7346,1169), (7347,1135), (7349,4937), (7355,6907), (7359,6335), (7361,3143), (7364,2372), (7367,6047), (7368,872), (7374,1446), (7376,7242), (7379,2591), (7380,4138), (7389,227), (7400,135), (7409,2345), (7412,362), (7415,3775), (7428,302), (7434,2383), (7439,2991), (7442,1333), (7445,4595), (7451,6343), (7452,7345), (7454,561), (7458,527), (7467,4543), (7484,5043), (7487,6143), (7488,3785), (7490,1129), (7491,4751), (7497,4429), (7502,6000), (7506,5374), (7508,3019), (7509,3445), (7521,3781), (7529,1521), (7550,1046), (7574,6115), (7577,2725), (7587,6895), (7589,971), (7593,7421), (7596,6414), (7598,4201), (7610,4339), (7613,4217), (7620,3856), (7629,1261), (7640,7026), (7641,4549), (7643,1383), (7653,245), (7656,3296), (7658,5670), (7667,5515), (7674,5379), (7676,2113), (7677,5791), (7683,7403), (7686,3268), (7689,2101), (7700,2772), (7701,7237), (7707,2503), (7710,4647), (7713,2947), (7719,1879), (7728,2847), (7730,1644), (7731,5543), (7736,872), (7739,2203), (7742,4370), (7745,3975), (7757,3277), (7760,329), (7761,793), (7775,3455), (7784,4883), (7785,4667), (7787,1431), (7797,6445), (7803,4243), (7806,2363), (7808,5462), (7809,1871), (7817,4945), (7824,2168), (7826,6422), (7841,1607), (7845,2599), (7847,679), (7850,984), (7853,2695), (7856,686), (7857,875), (7869,4271), (7872,3167), (7875,5315), (7880,6029), (7883,2903), (7896,3174), (7904,500), (7905,6427), (7907,1027), (7914,2253), (7925,3861), (7929,749), (7937,1637), (7967,6463), (7977,1313), (7982,7069), (8000,938), (8001,2533), (8006,2522), (8009,2515), (8013,593), (8033,1977), (8036,1388), (8042,174), (8046,5769), (8051,6439), (8057,1673), (8064,69), (8066,4572), (8072,7785), (8073,3097), (8082,1410), (8087,687), (8093,7397), (8096,2307), (8097,5149), (8102,6425), (8105,1099), (8114,6689), (8117,735), (8120,2791), (8121,6131), (8123,7295), (8130,558), (8133,4691), (8139,7915), (8141,357), (8144,1459), (8153,4011), (8156,4421), (8162,2570), (8166,2318), (8184,4743), (8186,6811), (8187,3079), (8193,175), (8211,7963), (8213,2681), (8220,6964), (8231,8007), (8235,3583), (8237,5821), (8241,4571), (8246,2501), (8250,2015), (8256,5007), (8259,755), (8270,2669), (8276,5069), (8283,6419), (8297,4893), (8301,997), (8307,2795), (8309,2499), (8312,2219), (8315,6991), (8327,5335), (8339,6243), (8342,902), (8348,613), (8352,1263), (8354,2099), (8360,4410), (8361,5351), (8370,2376), (8372,817), (8375,7919), (8384,5201), (8385,4105), (8402,1963), (8420,8052), (8421,6067), (8441,7277), (8444,6443), (8448,5731), (8457,1811), (8460,6940), (8462,4016), (8466,5958), (8469,37), (8477,8003), (8480,1915), (8499,1555), (8504,122), (8508,2812), (8513,1137), (8525,5037), (8526,442), (8537,669), (8541,5857), (8543,7839), (8544,1658), (8549,2021), (8558,7677), (8561,6347), (8562,7486), (8564,507), (8573,5693), (8574,6126), (8577,2089), (8579,751), (8586,8246), (8592,1383), (8595,4255), (8600,4293), (8601,5497), (8604,7233), (8612,6738), (8613,1381), (8619,6223), (8622,7181), (8625,985), (8627,7883), (8631,2399), (8634,4076), (8636,3926), (8652,8280), (8657,2415), (8660,4609), (8661,4261), (8667,8507), (8669,1161), (8673,2305), (8685,1187), (8688,6464), (8691,7751), (8693,7875), (8697,3769), (8706,6124), (8717,4015), (8721,2119), (8727,7943), (8738,5516), (8741,5289), (8744,6537), (8753,383), (8756,6413), (8757,4397), (8763,623), (8768,6371), (8771,8471), (8774,5369), (8786,4122), (8805,2383), (8813,6757), (8825,4421), (8828,2642), (8835,7867), (8837,1407), (8840,2666), (8841,2233), (8843,1595), (8846,5768), (8847,6895), (8858,563), (8864,1697), (8865,1495), (8868,6236), (8873,5557), (8880,7871), (8885,1543), (8891,5819), (8892,8199), (8894,8852), (8897,6195), (8907,6727), (8909,5857), (8915,5223), (8933,701), (8937,5417), (8939,4427), (8945,8575), (8955,883), (8961,4153), (8972,8780), (8978,1467), (8993,591), (9003,8819), (9005,8553), (9011,4599), (9014,1250), (9015,7055), (9018,7367), (9020,3867), (9024,5566), (9029,7821), (9041,8657), (9044,480), (9045,4205), (9053,175), (9054,7918), (9059,1923), (9083,2007), (9089,4225), (9090,1328), (9093,2791), (9095,7263), (9099,115), (9101,8231), (9102,622), (9107,4219), (9110,2605), (9111,6023), (9114,1784), (9120,4465), (9126,9111), (9128,3626), (9132,844), (9140,3798), (9143,4759), (9144,53), (9146,6919), (9147,8935), (9150,3919), (9168,971), (9173,4219), (9176,2947), (9182,3721), (9185,6435), (9186,7994), (9189,8377), (9203,7587), (9213,6311), (9219,6791), (9225,233), (9230,878), (9237,157), (9246,9129), (9248,8531), (9254,6786), (9264,8126), (9270,812), (9275,9123), (9279,895), (9281,1753), (9285,9067), (9288,2491), (9291,2323), (9293,6335), (9294,9126), (9300,724), (9311,5951), (9317,3867), (9320,6907), (9321,4283), (9353,7267), (9360,1702), (9362,3594), (9366,5698), (9368,2423), (9369,1225), (9378,5258), (9380,4370), (9387,4403), (9393,1985), (9401,857), (9402,6521), (9405,8407), (9408,8010), (9411,2471), (9413,879), (9417,7159), (9419,675), (9428,7158), (9429,9017), (9434,1154), (9435,2171), (9443,6471), (9464,4601), (9474,7370), (9477,2345), (9480,6171), (9491,1347), (9500,5303), (9506,2372), (9510,4548), (9512,4022), (9522,9489), (9525,1843), (9534,2670), (9537,7513), (9543,2863), (9545,6737), (9551,703), (9558,3878), (9563,6039), (9570,7703), (9573,1955), (9575,4335), (9578,4385), (9579,1403), (9584,1033), (9585,4285), (9591,6239), (9600,5725), (9603,7111), (9618,838), (9620,8705), (9623,6799), (9627,2843), (9632,2546), (9636,689), (9641,4453), (9645,2095), (9653,6621), (9656,7777), (9660,8459), (9665,6761), (9666,1828), (9668,8046), (9675,3127), (9684,5344), (9687,3583), (9689,5539), (9698,8604), (9701,791), (9704,1526), (9710,5847), (9714,1707), (9716,1533), (9726,2468), (9732,910), (9741,3821), (9753,5515), (9755,8455), (9758,1159), (9761,7113), (9767,5103), (9771,67), (9773,1181), (9774,7092), (9794,6633), (9797,3635), (9806,5637), (9809,6909), (9813,1453), (9816,619), (9818,2816), (9819,6695), (9827,6751), (9830,6111), (9834,2639), (9843,8219), (9849,2933), (9851,6567), (9861,2053), (9863,855), (9864,3981), (9867,5239), (9878,7799), (9894,9519), (9896,5103), (9899,3219), (9902,8472), (9905,3785), (9915,895), (9917,7429), (9918,9568), (9920,3863), (9933,5663), (9950,3469), (9966,834), (9981,9209), (9998,5682), (10002,2872), ...

3. Primes composed of all ones except for two zeros. The number (10^a-1)/9-10^b-10^c is an ænlic prime for (a,b,c) = (12,9,1), (24,19,11), (384,353,225), ... If there are more ænlic primes of this form, then a > 2050.

I'm not aware of any ænlic primes composed of all ones except for three (or more) zeros.

Tuesday, January 22

Long time comin'


I first queried The Mudcat Café about this piece of music in August 1999. The fact that I had been unable since then to elicit a credible lead [see the final paragraph in my blog here, the Google+ posts here and (a reprise of the blog item) here] has been a thorn in my side! This evening I was going through some random old-time favourites in my music library and I thought again to look for it. Google showed me the Mudcat link and I went there to see how long ago I had posted my question. As I advanced the thread I reached a January 2017 guest posting with the above YouTube link.

To be fair, Anderson's voice wasn't exactly how my mind had recreated the memory of it, but there was little doubt that this was the song that I had last heard on the radio circa 1970 — almost fifty years ago. The YouTube audio had been up since September 2013. Three-plus years for someone to link it to the Mudcat thread and two more years for me to notice it.

Over the years I had convinced myself that I would never know the artist/song before I died. But my faith in the internet has been somewhat restored and I can cross this difficult things-to-find task off my bucket list.

Thursday, January 17

My 200th Leyland prime find


In August 2016 I mentioned my 100th Leyland prime find. This morning I found my 200th. The graph (click on it for a better view) shows the number of decimal digits of those 200 primes as a function of the discovery date (the calendar years mark the start of those years). One may note the periods of relative inactivity where I was burdening my processors with other tasks. The upper-right plateau constitutes my "long compute" which will come in at just under two years when it's done in April of this year.