A066576 Composite Euclid numbers: numbers of the form p# + 1, where p# denotes the primorial of the prime p.

30031, 510511, 9699691, 223092871, 6469693231, 7420738134811, 304250263527211, 13082761331670031, 614889782588491411, 32589158477190044731, 1922760350154212639071, 117288381359406970983271

Offset: 1

Author

Joseph L. Pe, Jan 07 2002

Keywords

• nonn

Comments

30031 appears in Wells's "Curious and Interesting Numbers" as the smallest composite number of the form p# + 1.

References

• David Wells, "The Penguin Dictionary of Curious and Interesting Numbers," Revised Edition, Penguin Books, London, England, 1997, page 166.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..341

Crossrefs

Cf. A014545, A006862.

Programs

Magma

[a: n in [2..19]| not IsPrime(a) where a is 1+&*[NthPrime(k):k in [1..n]]]; // Marius A. Burtea, Feb 18 2020

Mathematica

Do[c = Product[ Prime[i], {i, 1, n}] + 1; If[ !PrimeQ[c], Print[c]], {n, 1, 20} ]

Extensions

Edited by Robert G. Wilson v, Jan 09 2002