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A057704 Primorial - 1 prime indices: integers n such that the n-th primorial minus 1 is prime. 17
2, 3, 5, 6, 13, 24, 66, 68, 167, 287, 310, 352, 564, 590, 620, 849, 1552, 1849, 67132, 85586 (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

Table of n, a(n) for n=1..20.

Chris K. Caldwell, Prime Pages: Database Search

Chris K. Caldwell, The top 20: primorial primes

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[500] (* 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 * A078203 A253647 A131825

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)

STATUS

approved

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Last modified December 9 14:46 EST 2016. Contains 278971 sequences.