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Revision History for A103783

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A103783

Primes of the form primorial P(k)*n-1 with minimal n, n>0, k>=2.
(history; published version)

#8 by Joerg Arndt at Tue Jul 03 16:01:28 EDT 2012

STATUS

proposed

approved

#7 by R. J. Mathar at Tue Jul 03 16:00:25 EDT 2012

STATUS

editing

proposed

#6 by R. J. Mathar at Tue Jul 03 16:00:08 EDT 2012

COMMENTS

Smallest prime p such that the prime factorization of p+1 contains the first n+1 primes. - R. J. Mathar, Jul 03 2012

CROSSREFS

Cf. A002110, A103515, A103782, A073917, A214089.

STATUS

approved

editing

#5 by Russ Cox at Sat Mar 31 10:23:47 EDT 2012

AUTHOR

_Lei Zhou (lzhou5(AT)emory.edu), _, Feb 15 2005

Discussion

Sat Mar 31

10:23

OEIS Server: https://oeis.org/edit/global/387

#4 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

MATHEMATICA

nmax = 2^2048; npd = 2; n = 2; npd = npd*Prime[n]; While[npd < nmax, tt = 1; cp = npd*tt - 1; While[(tt ≤ <= (Prime[n])^2) && (! (PrimeQ[cp])), tt = tt + 1; cp = npd*tt - 1]; Print[cp]; n = n + 1; npd = npd*Prime[n]]

KEYWORD

nonn,new

nonn

#3 by N. J. A. Sloane at Sun Jun 29 03:00:00 EDT 2008

OFFSET

2,1,1

KEYWORD

nonn,new

nonn

#2 by N. J. A. Sloane at Sat Apr 09 03:00:00 EDT 2005

MATHEMATICA

nmax = 2^2048; npd = 2; n = 2; npd = npd*Prime[n]; While[npd < nmax, tt = 1; cp = npd*tt - 1; While[(tt ≤ (Prime[n])^2) && (! (PrimeQ[cp])), tt = tt + 1; cp = npd*tt - 1]; Print[cp]; n = n + 1; npd = npd*Prime[n]]

KEYWORD

nonn,new

nonn

#1 by N. J. A. Sloane at Sun Feb 20 03:00:00 EST 2005

NAME

Primes of the form primorial P(k)*n-1 with minimal n, n>0, k>=2.

DATA

5, 29, 419, 2309, 30029, 1021019, 19399379, 669278609, 38818159379, 601681470389, 14841476269619, 304250263527209, 235489703970060539, 1844669347765474229, 228124109340330313109, 24995884552004764307909

OFFSET

2,1

COMMENTS

Weak conjecture: sequence is defined for all k>=2; strong conjecture: n<(prime(k))^2;

EXAMPLE

P(2)*1-1=5 is prime, so a(2)=5;

P(9)*3-1=669278609 is prime, so a(9)=669278609;

MATHEMATICA

CROSSREFS

Cf. A002110, A103515, A103782.

KEYWORD

nonn,new

AUTHOR

Lei Zhou (lzhou5(AT)emory.edu), Feb 15 2005

STATUS

approved