A267125 Numbers n such that n+2!, n+2!+3!, n+2!+3!+4!, n+2!+3!+4!+5!, n+2!+3!+4!+5!+6!, n+2!+3!+4!+5!+6!+7!, n+2!+3!+4!+5!+6!+7!+8!, n+2!+3!+4!+5!+6!+7!+8!+9!, and n+2!+3!+4!+5!+6!+7!+8!+9!+10! are all prime.
3525, 58755, 2171625, 3711201, 4612811, 4657289, 6714495, 7075271, 7687071, 9330381, 10523045, 11904249, 14060501, 16634171, 17191839, 22909971, 32351711, 35723709, 43992879, 45377325, 49031165, 56682171, 60219615, 64348635, 83743601, 86669615, 94265805
Offset: 1
Keywords
Examples
3525+2!=3527 (is prime) 3525+2!+3!=3533 (is prime) 3525+2!+3!+4!=3557 (is prime) 3525+2!+3!+4!+5!=3677 (is prime) 3525+2!+3!+4!+5!+6!=4397 (is prime) 3525+2!+3!+4!+5!+6!+7!=9437 (is prime) 3525+2!+3!+4!+5!+6!+7!+8!=49757 (is prime) 3525+2!+3!+4!+5!+6!+7!+8!+9!=412637 (is prime) 3525+2!+3!+4!+5!+6!+7!+8!+9!+10!=4041437 (is prime)
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
r = Accumulate@ Array[#! &, 9, 2]; fQ[n_] := Union[ PrimeQ[n + r]] == {True}; k = 1; lst = {}; While[k < 10^8, If[ fQ@ k, AppendTo[lst, k]]; k += 2]; lst (* Robert G. Wilson v, Jan 10 2016 *) -
PARI
is(n)=for(k=2,10,if(!isprime(n+=k!), return(0))); 1 \\ Charles R Greathouse IV, Feb 23 2016
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PARI
list(lim)=my(v=List(),p=2,q=3,g,n); forprime(r=5,lim+8, g=q-p; if(g>6 || (g<6 && r-p>6), p=q;q=r; next); n=p+6; for(k=4,10, if(!isprime(n+=k!), p=q;q=r;next(2))); listput(v,p-2);p=q;q=r); Vec(v) \\ Charles R Greathouse IV, Feb 23 2016
Extensions
a(11) onward from Robert G. Wilson v, Jan 10 2016