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A106488
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.
1
641, 1788, 1918, 3731, 7093, 8009, 22770, 28600
OFFSET
1,1
COMMENTS
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)
CROSSREFS
Sequence in context: A252434 A105130 A117129 * A259997 A256806 A206164
KEYWORD
base,nonn,more
AUTHOR
Jason Earls, May 29 2005
EXTENSIONS
a(7)-a(8) from Michael S. Branicky, Sep 20 2024
STATUS
approved