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A014545
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Primorial primes: n such that n-th Euclid number (A006862(n)) = 1 + (Product of first n primes) is prime.
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35
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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
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0,2
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COMMENTS
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The prime referenced by the final term of the sequence above (a(21) = 33237) has 169966 digits. [From Harvey P. Dale, May 04 2012]
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REFERENCES
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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. 1-2-3, 1997, 170-183.
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LINKS
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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
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EXAMPLE
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p(4413)=42209 and Primorial(4413)+1=42209#+1 is a 18241-digit prime. Also p(13494)=145823 and Primorial(13494)+1 = 145823#+1 is a 63142-digit prime.
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MATHEMATICA
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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 *)
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PROG
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(PARI) is(n)=ispseudoprime(prod(i=1, n, prime(i))+1) \\ Charles R Greathouse IV, Mar 21 2013
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CROSSREFS
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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 A135323
Adjacent sequences: A014542 A014543 A014544 * A014546 A014547 A014548
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KEYWORD
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nonn,nice,hard
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AUTHOR
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Eric W. Weisstein, bremner(AT)snoopy.usask.ca (Murray Bremner)
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EXTENSIONS
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More terms from Labos E. (labos(AT)ana.sote.hu). 13494 from Arlin Anderson (starship1(AT)gmail.com), Oct 20, 2000.
31260, 33237 from Eric W. Weisstein, Mar 13 2004 (based on information in A057704)
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STATUS
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approved
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