A108055 Numbers n such that 1_100.2_200.3_300 ... 8_800.9_900.10^n+1 is prime, i.e., 1 repeated 100 times, concatenated with 2 repeated 200 times, etc.

2395, 3980, 4584, 9073, 12115

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)

Links

Table of n, a(n) for n=1..5.

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

Crossrefs

Cf. A106488.

Sequence in context: A115931 A323344 A323341 * A286342 A204357 A043420

Adjacent sequences: A108052 A108053 A108054 * A108056 A108057 A108058

Keyword

base,nonn,more

Author

Jason Earls, Jun 02 2005

Status

approved