

A071580


Smallest prime of the form k*a(n1)*a(n2)*...*a(1)+1.


5




OFFSET

1,1


COMMENTS

The former definition was "Smallest prime == 1 mod (a(n1)*a(n2)*...*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 "N1 method" since the full factorization of a(n)1 is known.  Jeppe Stig Nielsen, May 14 2023


LINKS



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:


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



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



