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A057704 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(19) > 25000. - Robert Price, Nov 22 2014

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..18.

PrimeGrid, The top 20: primorial primes

Eric Weisstein's World of Mathematics, Primorial

Eric Weisstein's World of Mathematics, Integer Sequence Primes

Wikipedia, Primorial prime

FORMULA

a(n) = A000720(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 *)

CROSSREFS

Cf. A006794, 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,changed

AUTHOR

Labos Elemer, Oct 24 2000

EXTENSIONS

Corrected by Holzer Werner, Nov 28 2002

STATUS

approved

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Last modified August 29 10:37 EDT 2015. Contains 261188 sequences.