Search: id:A066735
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%I A066735
%S A066735 2,3,19,1471,3001
%N A066735 Primes p dividing 1 + the product of the primes less than p.
%C A066735 Comment from Levai Gabor [L'{e}vai G'{a}bor], (gablevai(AT)vipmail.hu), 
               Nov 23, 2004: "Let p(1)=2, p(2)=3, p(3)=5, ... denote the primes 
               and let E(n) = 1 + p(1) * p(2) * ... * p(n). For k >= 1, list the 
               primes p such that p(n+k) | E(n). For k=1 we get this sequence, for 
               k=2 we get A100465.
%C A066735 "For k >= 3 the known results are as follows: if k = 3: no solutions 
               for p < 80000000; if k = 4: 463, 2908123 and no others for p < 80000000; 
               if k = 5: 61, 73 and no others for p < 80000000; if k = 6: 21687203 
               and no others for p < 80000000; if k = 7: 149, 43951591 and no others 
               for p < 80000000; if k = 8: 31, 131 and no others for p < 80000000; 
               if k = 9: 58691999 and no others for p < 80000000."
%H A066735 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/
               matha1/matha102.htm">Factorization results for #Pn (Primorial) + 
               1</a>
%e A066735 1 + Product of the primes < 19 = 1 + 2*3*5*7*11*13*17 = 510511 = 19*26869; 
               so 19 is a term of the sequence.
%t A066735 p = 2; Do[q = Prime[n]; If[ IntegerQ[(p + 1)/q], Print[q]]; p = p*q, 
               {n, 2, 86120} ]
%o A066735 (PARI) a066735(m) =local(k,p); k=1; forprime(p=2,m, if((k+1)%p==0,print1(p,
               ",")); k=k*p)
%Y A066735 Cf. A002110, A002585, A100465.
%Y A066735 Sequence in context: A048827 A032077 A014547 this_sequence A099069 A038584 
               A108022
%Y A066735 Adjacent sequences: A066732 A066733 A066734 this_sequence A066736 A066737 
               A066738
%K A066735 nonn
%O A066735 1,1
%A A066735 Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Jan 15 2002
%E A066735 No further terms up to prime(216816) = 2999999. Is the sequence finite? 
               - Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 17 2002
%E A066735 No further terms up to 80000000. - Levai Gabor [L'{e}vai G'{a}bor], (gablevai(AT)vipmail.hu), 
               Nov 23, 2004

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