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A071580
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Smallest prime of the form k*a(n-1)*a(n-2)*...*a(1)+1.
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5
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OFFSET
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1,1
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COMMENTS
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The former definition was "Smallest prime == 1 mod (a(n-1)*a(n-2)*...*a(1)) for n>=2 with a(1)=2."
a(6) through a(13), with digit lengths 8, 16, 32, 63, 127, 253, 507 and 1012, respectively, have been certified prime with Primo.
There is no need to use Elliptic curve primality proving (ECPP) to certify the primes. The primality of each term can be proved recursively with the "N-1 method" since the full factorization of a(n)-1 is known. - Jeppe Stig Nielsen, May 14 2023
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LINKS
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MAPLE
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P:= 1:
for n from 1 to 13 do
for k from 1 do
if isprime(k*P+1) then
A[n]:= k*P+1;
P:= P * A[n];
break
fi
od
od:
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MATHEMATICA
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sp[{p_, a_}]:=Module[{k=1}, While[!PrimeQ[k*p+1], k++]; {p(p*k+1), p*k+1}]; NestList[sp, {2, 2}, 10][[All, 2]] (* Harvey P. Dale, Mar 04 2019 *)
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PROG
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(PARI) terms=13; v=vector(terms); p=2; v[1]=p; for(n=2, terms, q=p+1; while(!isprime(q), q=q+p); v[n]=q; p=p*q); v
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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