A066735 Primes p dividing 1 + the product of the primes less than p.

2, 3, 19, 1471, 3001

Offset: 1

Author

Joseph L. Pe, Jan 15 2002

Keywords

• nonn
• more

Comments

No further terms up to prime(216816) = 2999999. Is the sequence finite? - Klaus Brockhaus, Jan 17 2002

From Lévai Gábor (gablevai(AT)vipmail.hu), Nov 23 2004: (Start)

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.

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. (End)

No further terms up to 80000000. - Lévai Gábor (gablevai(AT)vipmail.hu), Nov 23 2004

a(6) > 179424673 = prime(10^7). - Giovanni Resta, Apr 13 2017

a(6) > 914799232 > prime(46727379). - Max Z. Scialabba, Feb 26 2024

Examples

			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.
		

Links

• Hisanori Mishima, Factorization results for #Pn (Primorial) + 1

Crossrefs

Cf. A002110, A002585, A100465, A081618.

Programs

Mathematica

p = 2; Do[q = Prime[n]; If[ IntegerQ[(p + 1)/q], Print[q]]; p = p*q, {n, 2, 86120} ]

PARI

a066735(m) =local(k,p); k=1; forprime(p=2,m, if((k+1)%p==0,print1(p,",")); k=k*p)