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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

Table of n, a(n) for n=1..29.

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 July 24 13:42 EDT 2021. Contains 346273 sequences. (Running on oeis4.)