

A014545


Primorial primes: n such that nth Euclid number (A006862(n)) = 1 + (Product of first n primes) is prime.


35



1, 2, 3, 4, 5, 11, 75, 171, 172, 384, 457, 616, 643, 1391, 1613, 2122, 2647, 2673, 4413, 13494, 31260, 33237
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OFFSET

0,2


COMMENTS

The prime referenced by the final term of the sequence above (a(21) = 33237) has 169966 digits.  Harvey P. Dale, May 04 2012


REFERENCES

J.M. De Koninck, Ces nombres qui nous fascinent, Entry 211, p. 61, Ellipses, Paris 2008.
H. Ibstedt, A Few Smarandache Sequences, Smarandache Notions Journal, Vol. 8, No. 123, 1997, 170183.


LINKS

Table of n, a(n) for n=0..21.
C. K. Caldwell, Primorial Primes
Eric Weisstein's World of Mathematics, Euclid Number
Eric Weisstein's World of Mathematics, Primorial
Eric Weisstein's World of Mathematics, Integer Sequence Primes


EXAMPLE

p(4413)=42209 and Primorial(4413)+1=42209#+1 is a 18241digit prime. Also p(13494)=145823 and Primorial(13494)+1 = 145823#+1 is a 63142digit prime.


MATHEMATICA

Flatten[Position[Rest[FoldList[Times, 1, Prime[Range[180]]]]+1, _?PrimeQ]] (* From Harvey P. Dale, May 04 2012 *) (* this program generates the first 9 terms of the sequence; changing the Range constant to 33237 will generate all 22 terms above, but it will take a long time to do so *)


PROG

(PARI) is(n)=ispseudoprime(prod(i=1, n, prime(i))+1) \\ Charles R Greathouse IV, Mar 21 2013


CROSSREFS

A005234 gives same sequence in another form, namely values of p such that 1 + product of primes <= p is prime. Cf. A002110, A006862, A057704. A018239 gives the actual primes.
Sequence in context: A032988 A190783 A136367 * A158930 A065636 A229347
Adjacent sequences: A014542 A014543 A014544 * A014546 A014547 A014548


KEYWORD

nonn,nice,hard


AUTHOR

Eric W. Weisstein, Murray R. Bremner


EXTENSIONS

More terms from Labos Elemer
a(19) from Arlin Anderson (starship1(AT)gmail.com), Oct 20 2000
a(20), a(21) from Eric W. Weisstein, Mar 13 2004 (based on information in A057704)


STATUS

approved



