

A057704


Primorial  1 prime indices: integers n such that the nth primorial minus 1 is prime.


17



2, 3, 5, 6, 13, 24, 66, 68, 167, 287, 310, 352, 564, 590, 620, 849, 1552, 1849
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OFFSET

1,1


COMMENTS

Additional terms are known to include 67132 and 85586.  Eric W. Weisstein, Nov 03 2015
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.
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)).


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(P1) 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 (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


STATUS

approved



