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%I #38 Apr 14 2022 11:13:07
%S 2,3,5,7,11,101,17977,10619863,6620830889,80630964769,228204732751,
%T 1171432692373,1398341745571,10963707205259,15285151248481,
%U 10657331232548839,790738119649411319,18987964267331664557,74878248419470886233,1394313503224447816939
%N Prime partition numbers.
%H Alois P. Heinz, <a href="/A049575/b049575.txt">Table of n, a(n) for n = 1..100</a>
%H Ernest G. Hibbs, <a href="https://www.proquest.com/openview/4012f0286b785cd732c78eb0fc6fce80">Component Interactions of the Prime Numbers</a>, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.
%H G. K. Patil, <a href="https://web.archive.org/web/20150911053452/http://www.ijsres.com/2014/vol-1_issue-6/paper_8.pdf">Ramanujan's Life And His Contributions In The Field Of Mathematics</a>, International Journal of Scientific Research and Engineering Studies (IJSRES), 1(6) (2014), ISSN: 2349-8862.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PartitionFunctionPCongruences.html">Partition Function P Congruences</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PartitionFunctionP.html">Partition Function P</a>.
%F a(n) = A000041(A046063(n)) = A000040(A051143(n)). - _M. F. Hasler_, Oct 19 2008
%F A010051(a(n))*A167392(a(n)) = 1. - _Reinhard Zumkeller_, Nov 03 2009
%t lst={};Do[a=PartitionsP[n];If[PrimeQ[a],AppendTo[lst,a]],{n,2*6!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jun 14 2009 *)
%t Select[PartitionsP[Range[1000]],PrimeQ] (* _Harvey P. Dale_, Mar 11 2013 *)
%o (PARI) for(n=0,10^3,my(p=numbpart(n));if(isprime(p),print1(p,", "))); \\ _Joerg Arndt_, May 09 2013
%Y Intersection of A000040 and A000041.
%Y Cf. A046063, A051143.
%Y Cf. A038753, A065728. - _Reinhard Zumkeller_, Nov 03 2009
%K nonn,nice
%O 1,1
%A _G. L. Honaker, Jr._
%E More terms from _James A. Sellers_ and _Christian G. Bower_, Oct 15 1999.
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