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.

641, 1788, 1918, 3731, 7093, 8009, 22770, 28600, 91321, 93760

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)

Numbers k such that ((10^6660 - 10^667 + 9)/(9*10^666 - 9))*10^k + 1 is prime. - Jason Yuen, Sep 19 2025

a(11) > 150000. - Jason Yuen, Oct 04 2025

Links

Table of n, a(n) for n=1..10.

Rudolf Ondrejka, The Top Ten: a Catalogue of Primal Configurations.

Crossrefs

Cf. A108055.

Sequence in context: A252434 A105130 A117129 * A259997 A256806 A206164

Adjacent sequences: A106485 A106486 A106487 * A106489 A106490 A106491

Keyword

base,nonn,more,hard

Author

Jason Earls, May 29 2005

Extensions

a(7)-a(8) from Michael S. Branicky, Sep 20 2024

Name edited by Michael S. Branicky, Sep 19 2025

a(9)-a(10) from Jason Yuen, Oct 04 2025

Status

approved