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Search: id:A076670
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| A076670 |
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Prime divisors of (10^9)^(10^9) + 1 = 10^9000000000 + 1. |
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+0
1
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| 39937, 64513, 921601, 1514497, 9188353, 11059201, 23500801, 25159681, 99328001, 288000001, 302078977, 593920001, 864000001, 14400000001, 16002416641, 27769098241, 35904000001, 61120000001, 61600000001
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OFFSET
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1,1
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COMMENT
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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).
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REFERENCES
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NZ Science Monthly Bulletin Board, advert., 2000.
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LINKS
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S. S. Wagstaff, The Cunningham Project
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EXAMPLE
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a(1)= 39937 because 39937 divides (10^9)^(10^9)+1.
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MATHEMATICA
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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}]
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PROGRAM
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(PARI) for(k=1, 20000, p=2^10* k + 1; if (modpow(10^9, 10^9, p)+1==p, print(p), ))
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CROSSREFS
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Cf. A055386 (least prime factor of (2n)^(2n) + 1 ).
Adjacent sequences: A076667 A076668 A076669 this_sequence A076671 A076672 A076673
Sequence in context: A004671 A116220 A103809 this_sequence A106772 A015328 A126104
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KEYWORD
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more,nonn,fini
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AUTHOR
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Donald S. McDonald (don.mcdonald(AT)paradise.net.nz), Oct 25 2002
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EXTENSIONS
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Thanks for help from Kurt Foster and Bob Backstrom (Australia) - DSMcD.
Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 13 2002
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