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 A057704 Primorial - 1 prime indices: integers m such that the m-th primorial minus 1 is prime. 20
 2, 3, 5, 6, 13, 24, 66, 68, 167, 287, 310, 352, 564, 590, 620, 849, 1552, 1849, 67132, 85586, 234725 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS There are two versions of "primorial": this is using the definition in A002110. - Robert Israel, Dec 30 2014 As of 28 February 2012, the largest known primorial prime is A002110(85586) - 1 with 476311 digits, found by the PrimeGrid project (see link). - Dmitry Kamenetsky, Aug 11 2015 LINKS Chris K. Caldwell, Prime Pages: Database Search Chris K. Caldwell, The top 20: primorial primes Sílvia Casacuberta, On the divisibility of binomial coefficients, arXiv:1906.07652 [math.NT], 2019. Mentions this sequence. Benny Lim, Prime Numbers Generated From Highly Composite Numbers, Parabola (2018) Vol. 54, Issue 3. Eric Weisstein's World of Mathematics, Integer Sequence Primes Eric Weisstein's World of Mathematics, Primorial Prime Wikipedia, Primorial prime FORMULA a(n) = A000720(A006794(n)). a(n) = primepi(A006794(n)). EXAMPLE The 6th primorial is A002110(6) = 2*3*5*7*11*13 = 30030, and 30030 - 1 = 30029 is a prime, so 6 is in the sequence. MAPLE P:= 1: p:= 1: count:= 0: for n from 1 to 1000 do   p:= nextprime(p);   P:= P*p;   if isprime(P-1) then     count:= count+1;     A[count]:= n;   fi od: seq(A[i], i=1..count); # Robert Israel, Dec 25 2014 MATHEMATICA a057704[n_] := Flatten@Position[ Rest[FoldList[Times, 1, Prime[Range[n]]]] - 1, _Integer?PrimeQ]; a057704 (* Michael De Vlieger, Dec 25 2014 *) PROG (PARI) lista(nn) = {s = 1; for(k=1, nn, s *= prime(k); if(ispseudoprime(s - 1), print1(k, ", ")); ); } \\ Altug Alkan, Dec 08 2015 (PARI) is(n) = ispseudoprime(prod(k=1, n, prime(k)) - 1); \\ Altug Alkan, Dec 08 2015 CROSSREFS Cf. A006794 (Primorial -1 primes: Primes p such that -1 + product of primes up to p is prime). Cf. A057705, A014545, A005234, A002110, A057706. Sequence in context: A098833 A075371 A218948 * A281382 A078203 A285937 Adjacent sequences:  A057701 A057702 A057703 * A057705 A057706 A057707 KEYWORD nonn,more AUTHOR Labos Elemer, Oct 24 2000 EXTENSIONS Corrected by Holzer Werner, Nov 28 2002 a(19)-a(20) from Eric W. Weisstein, Dec 08 2015 (Mark Rodenkirch confirms based on saved log files that all p < 700,000 have been tested) a(21) from Jeppe Stig Nielsen, Oct 19 2021 STATUS approved

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Last modified January 24 00:05 EST 2022. Contains 350515 sequences. (Running on oeis4.)