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A071580 Smallest prime of the form k*a(n-1)*a(n-2)*...*a(1)+1. 5
2, 3, 7, 43, 3613, 65250781, 5109197227031017, 21753246920584523633819544186061, 993727878334632126576336773629979379563850938567846991629270287 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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
LINKS
Mersenne Forum, A071580
MAPLE
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:
seq(A[i], i=1..13); # Robert Israel, May 19 2015
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Sequence in context: A129871 A075442 A082993 * A359340 A267507 A344561
KEYWORD
nonn
AUTHOR
Rick L. Shepherd, May 31 2002
EXTENSIONS
Definition reworded by Andrew R. Booker, May 19 2015
STATUS
approved

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Last modified April 20 06:53 EDT 2024. Contains 371799 sequences. (Running on oeis4.)