A106488 - OEIS

%I #13 Sep 21 2024 02:29:56

%S 641,1788,1918,3731,7093,8009,22770,28600

%N Numbers k such that 1_666.2_666.3_666 ... 8_666.9_666.10^k+1 is prime, i.e., 1 repeated 666 times, concatenated with 2 repeated 666 times, etc.

%C These are "subscript" primes, similar to those listed in Table 30 of the Primal Configurations document. Only 3731, 7093 and 8009 have been proved prime. The others are Fermat and Lucas PRPs. Primality proof for the largest (14003 digits): PFGW Version 20041001.Win_Stable (v1.2 RC1b) [FFT v23.8] Primality testing (r(666,1)*10^5328+r(666,2)*10^4662+r(666,3)*10^3996+r(666,4)*10^3330+r(666,5)*10^2664+r(666,6)*10^1998+r(666,7)*10^1332+r(666,8)*10^666+r(666,9))*10^8009+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 17 (r(666,1)*10^5328+r(666,2)*10^4662+r(666,3)*10^3996+r(666,4)*10^3330+r(666,5)*10^2664+r(666,6)*10^1998+r(666,7)*10^1332+r(666,8)*10^666+r(666,9))*10^8009+1 is prime! (38.8002s+0.0106s)

%H R. Ondrejka, <a href="http://www.utm.edu/research/primes/lists/top_ten/">The Top Ten: a Catalogue of Primal Configurations</a>.

%K base,nonn,more

%O 1,1

%A _Jason Earls_, May 29 2005

%E a(7)-a(8) from _Michael S. Branicky_, Sep 20 2024