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 A076670 Prime divisors of (10^9)^(10^9) + 1 = 10^9000000000 + 1. 0
 39937, 64513, 921601, 1514497, 9188353, 11059201, 23500801, 25159681, 99328001, 288000001, 302078977, 593920001, 864000001, 14400000001, 16002416641, 27769098241, 35904000001, 61120000001, 61600000001, 90708480001, 164457013249, 249832960001, 16281309920257, 16598085949441, 22574752000001, 39315840000001, 132379043573761, 182544000000001, 230846400000001 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Numbers of the form 10^{10h}+1 can be algebraically factored into (10^{2h}+1)*L*M, L=A-B, M=A+B, h=2k-1, A=10^{4h}+5.10^{3h}+7.10^{2h}+5.10^h+1, B=10^k(10^{3h}+2.10^{2h}+2.10^h+1). Cyclotomic factorization: 10^(9*10^9)+1 = \prod_{d|9*5^9} \Phi_{1024*d}(10). Every term is congruent to 1 modulo 1024. - Max Alekseyev, Apr 28 2013 a(30) > 10^15. - Max Alekseyev, Jul 02 2013 Contains 3611707318387778163302401 (a factor of 10^512+1). - Max Alekseyev, Jan 07 2015 REFERENCES NZ Science Monthly Bulletin Board, advert., 2000. LINKS S. S. Wagstaff, The Cunningham Project EXAMPLE a(1)= 39937 because 39937 divides (10^9)^(10^9)+1. MATHEMATICA NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; p = 2; Do[ While[ PowerMod[10, 9000000000, p] + 1 != p, p = NextPrim[p]]; Print[p]; p++, {n, 1, 19}] PROG (PARI) forstep(p=1, 10^14, 1024, if(!ispseudoprime(p), next); if(Mod(10, p)^9000000000==-1, print(p)); ) CROSSREFS Cf. A055386 (least prime factor of (2n)^(2n) + 1 ). Sequence in context: A257185 A254985 A210386 * A251757 A250334 A250909 Adjacent sequences:  A076667 A076668 A076669 * A076671 A076672 A076673 KEYWORD nonn,fini AUTHOR Donald S. McDonald, Oct 25 2002 EXTENSIONS Thanks for help from Kurt Foster and Bob Backstrom (Australia) - Donald S. McDonald Edited and extended by Robert G. Wilson v, Nov 13 2002 Definition corrected by Sean A. Irvine, Feb 16 2010 Definition corrected by Max Alekseyev, Apr 28 2010 a(20)-a(26) from Max Alekseyev, Apr 28 2013 a(27)-a(29) from Max Alekseyev, Jul 02 2013 STATUS approved

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Last modified December 5 10:26 EST 2020. Contains 338945 sequences. (Running on oeis4.)