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A108055
Numbers k such that (1_100.2_200.3_300 ... 8_800.9_900)*10^k + 1 is prime, i.e., 1 repeated 100 times, concatenated with 2 repeated 200 times, etc.
1
2395, 3980, 4584, 9073, 12115, 22055, 26457
OFFSET
1,1
COMMENTS
These are "subscript" primes, similar to those listed in Table 30 of the Primal Configurations document. All have been proved prime. Primality proof for the largest (16615 digits): PFGW Version 20041001.Win_Stable (v1.2 RC1b) [FFT v23.8] Primality testing (r(100,1)*10^4400+r(200,2)*10^4200+r(300,3)*10^3900+r(400,4)*10^3500+r(500,5)*10^3000+r(600,6)*10^2400+r(700,7)*10^1700+r(800,8)*10^900+r(900,9))*10^12115+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 13 Calling Brillhart-Lehmer-Selfridge with factored part 50.97% (r(100,1)*10^4400+r(200,2)*10^4200+r(300,3)*10^3900+r(400,4)*10^3500+r(500,5)*10^3000+r(600,6)*10^2400+r(700,7)*10^1700+r(800,8)*10^900+r(900,9))*10^12115+1 is prime! (46.2683s+0.0076s)
CROSSREFS
Cf. A106488.
Sequence in context: A115931 A323344 A323341 * A286342 A204357 A043420
KEYWORD
base,nonn,hard,more
AUTHOR
Jason Earls, Jun 02 2005
EXTENSIONS
Name edited by and a(6)-a(7) from Michael S. Branicky, Sep 19 2025
STATUS
approved