A117844 Primes generated from a gamma function based formula: very large primes from factorial level numbers like the Euclid n!+1 type of prime.

3, 19, 6652799, 3779, 831599, 108972863999, 32432399, 538583682060103679999, 115783667999, 79196028911999, 113425723441857835007999999, 9899503613999, 10098444038626943999999, 8960776752100485056195299206758399999999

Offset

0,1

Comments

Gives 31% primes from ten levels the last one with 39 powers of ten. alength = Length[a]*(Length[a] - 1)/2=45 N[Length[b]/alength]=0.311111 (*Decimal digit length*) Floor[Log[b]/Log[10]] {0, 1, 6, 3, 5, 11, 7, 20, 11, 13, 26, 12, 22, 39}

Links

Table of n, a(n) for n=0..13.

Formula

f[n_, m_] = FullSimplify[((4/3)*Gamma[2*(n + m)]/(2^m*2^(2*(n - m))))] - 1 a(n) = If[PrimeQ[f[i,j]]=True,f[i,j]]

Mathematica

f[n_, m_] = FullSimplify[((4/3)*Gamma[2*(n + m)]/(2^m*2^(2*(n - m))))] - 1 a = Table[Table[If[PrimeQ[f[n, m]], f[n, m], {}], {m, 1, n}], {n, 1, 10}] b = Flatten[a]

Crossrefs

Sequence in context: A191623 A164063 A092828 * A260371 A067607 A013332

Adjacent sequences: A117841 A117842 A117843 * A117845 A117846 A117847

Keyword

nonn,uned

Author

Roger L. Bagula, Apr 30 2006

Status

approved