login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A002585 Largest prime factor of 1 + (product of first n primes).
(Formerly M2697 N1081)
10
3, 7, 31, 211, 2311, 509, 277, 27953, 703763, 34231, 200560490131, 676421, 11072701, 78339888213593, 13808181181, 18564761860301, 19026377261, 525956867082542470777, 143581524529603, 2892214489673, 16156160491570418147806951, 96888414202798247, 1004988035964897329167431269 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Based on Euclid's proof that there are infinitely many primes.

The products of the first primes are called primorial numbers. - Franklin T. Adams-Watters, Jun 12 2014

REFERENCES

M. Kraitchik, On the divisibility of factorials, Scripta Math., 14 (1948), 24-26 (but beware errors).

M. Kraitchik, Introduction à la Théorie des Nombres. Gauthier-Villars, Paris, 1952, p. 2.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Sean A. Irvine, Table of n, a(n) for n = 1..81

A. Borning, Some results for k!+-1 and 2.3.5...p+-1, Math. Comp., 26 (1972), 567-570.

M. Kraitchik, On the divisibility of factorials, Scripta Math., 14 (1948), 24-26 (but beware errors). [Annotated scanned copy]

S. Kravitz and D. E. Penney, An extension of Trigg's table, Math. Mag., 48 (1975), 92-96.

S. Kravitz and D. E. Penney, An extension of Trigg's table, Math. Mag., 48 (1975), 92-96. [Annotated scanned copy; also letter from N. J. A. Sloane to John Selfridge]

R. 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, 2012 - From N. J. A. Sloane, Jun 13 2012

Hisanori Mishima, Factorizations of many number sequences

Hisanori Mishima, Factorizations of many number sequences

John Selfridge, Marvin Wunderlich, Robert Morris, N. J. A. Sloane, Correspondence, 1975

Eric Weisstein's World of Mathematics, Euclid Number.

R. G. Wilson v, Explicit factorizations

MATHEMATICA

FactorInteger[#][[-1, 1]]&/@Rest[FoldList[Times, 1, Prime[Range[30]]]+1] (* Harvey P. Dale, Apr 10 2012 *)

PROG

(PARI) a(n)=my(f=factor(prod(i=1, n, prime(i))+1)[, 1]); f[#f] \\ Charles R Greathouse IV, Feb 07 2017

CROSSREFS

Cf. A002584, A051342, A002110.

Sequence in context: A059296 A123332 A051342 * A103785 A289127 A289125

Adjacent sequences:  A002582 A002583 A002584 * A002586 A002587 A002588

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Labos Elemer, May 02 2000

More terms from Robert G. Wilson v, Mar 24 2001

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 20 12:37 EST 2018. Contains 317402 sequences. (Running on oeis4.)