A057705 Primorial primes: primes p such that p+1 is a primorial number (A002110).

5, 29, 2309, 30029, 304250263527209, 23768741896345550770650537601358309, 19361386640700823163471425054312320082662897612571563761906962414215012369856637179096947335243680669607531475629148240284399976569

Offset

1,1

Links

Bill McEachen, Table of n, a(n) for n = 1..11

Chris K. Caldwell's The Top Twenty, Primorial.

Romeo Mestrovic, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, arXiv preprint arXiv:1202.3670 [math.HO], 2012. - N. J. A. Sloane, Jun 13 2012

Formula

a(n) = A002110(A057704(n)) - 1.

Mathematica

Select[FoldList[Times, 1, Prime[Range[70]]], PrimeQ[# - 1] &] - 1 (* Harvey P. Dale, Jan 27 2014 *)

Prog

(Haskell)
a057705 n = a057705_list !! (n-1)
a057705_list = filter ((== 1) . a010051) a057588_list
-- Reinhard Zumkeller, Mar 27 2013
(PARI)
default(nbthreads, 6)
build_primorials(n)={my(acc=1, v=vector(n)); for(k=1, n, acc*=prime(k); v[k]=acc); v; }
less1(x)=if(isprime(x-1), x-1, 0);
listaa(pm=67)={my(primorials=build_primorials(pm));
my(hits=parapply(less1, primorials)); \\multithread
select(x->x>0, hits); } \\ Bill McEachen, May 17 2026

Crossrefs

See A006794 and A057704 (the main entries for this sequence) for more terms.

Cf. A014545, A018239.

Cf. A002110, A010051.

Subsequence of A057588.

Sequence in context: A057208 A175905 A057706 * A237188 A371347 A086720

Adjacent sequences: A057702 A057703 A057704 * A057706 A057707 A057708

Keyword

nonn,nice

Author

Labos Elemer, Oct 24 2000

Status

approved