## Sunday, August 26, 2018

### More ænlic primes

When I presented ænlic primes earlier this month I pointed to the remarkable stability of the number of ænlic primes for a given digit-length. I noted that — except for four near-the-start values — they are always greater than 20 and less than 48. Last week I finished my search to 10^500, netting a total of 16115 ænlic primes thereto. As a result, the "greater than 20" needs to be adjusted to "greater than 17". Still, the overall trend continued and I decided to spend another week angling for the counts of 660- to 670-digit ænlic primes and — at intervals of ten, as a bridge — from 510- to 650-digit counts:

As icing on the cake, I did the 1000-digit ænlic primes. I found 36:

(10^1000 - 1)/9 + 7*10^463
2*(10^1000 - 1)/9 - 2*10^647 - 1
2*(10^1000 - 1)/9 - 2*10^192 + 7
2*(10^1000 - 1)/9 + 6*10^239 - 1
2*(10^1000 - 1)/9 + 3*10^251 + 5
2*(10^1000 - 1)/9 +   10^344 + 1
2*(10^1000 - 1)/9 + 4*10^641 + 7
2*(10^1000 - 1)/9 + 6*10^969 + 5
3*(10^1000 - 1)/9 - 2*10^150
3*(10^1000 - 1)/9 + 5*10^481
3*(10^1000 - 1)/9 + 2*10^759
4*(10^1000 - 1)/9 - 4*10^777 + 5
4*(10^1000 - 1)/9 -   10^712 - 1
4*(10^1000 - 1)/9 + 5*10^ 64 + 5
4*(10^1000 - 1)/9 + 4*10^192 + 5
4*(10^1000 - 1)/9 + 4*10^516 + 3
4*(10^1000 - 1)/9 +   10^738 + 3
4*(10^1000 - 1)/9 +   10^796 + 5
4*(10^1000 - 1)/9 + 2*10^930 + 5
5*(10^1000 - 1)/9 - 3*10^812 - 4
5*(10^1000 - 1)/9 - 5*10^485 + 2
5*(10^1000 - 1)/9 - 2*10^ 41 + 2
5*(10^1000 - 1)/9 +   10^611 + 4
6*(10^1000 - 1)/9 - 6*10^799 + 1
6*(10^1000 - 1)/9 - 6*10^461 - 5
6*(10^1000 - 1)/9 - 4*10^170 - 3
6*(10^1000 - 1)/9 - 2*10^161 - 3
6*(10^1000 - 1)/9 + 2*10^284 + 3
6*(10^1000 - 1)/9 + 2*10^891 - 3
7*(10^1000 - 1)/9 - 5*10^517
7*(10^1000 - 1)/9 +   10^538
4*(10^1000 - 1)/9 + 4*10^999 - 3
8*(10^1000 - 1)/9 -   10^401 + 1
8*(10^1000 - 1)/9 - 2*10^337 - 7
8*(10^1000 - 1)/9 - 8*10^125 - 1
8*(10^1000 - 1)/9 - 6*10^ 88 - 1