

A058013


Smallest prime p such that (n+1)^p  n^p is prime.


9



2, 2, 2, 3, 2, 2, 7, 2, 2, 3, 2, 17, 3, 2, 2, 5, 3, 2, 5, 2, 2, 229, 2, 3, 3, 2, 3, 3, 2, 2, 5, 3, 2, 3, 2, 2, 3, 3, 2, 7, 2, 3, 37, 2, 3, 5, 58543, 2, 3, 2, 2, 3, 2, 2, 3, 2, 5, 3, 4663, 54517, 17, 3, 2, 5, 2, 3, 3, 2, 2, 47, 61, 19, 23, 2, 2, 19, 7, 2, 7, 3, 2, 331, 2, 179, 5, 2, 5, 3, 2, 2
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OFFSET

1,1


COMMENTS

The terms a(47) and a(60) [were] unknown. The sequence continues at a(48): 2, 3, 2, 2, 3, 2, 2, 3, 2, 5, 3, 4663, a(60)=?, continued at a(61): 17, 3, 2, 5, 2, 3, 3, 2, 2, 47, 61, 19, 23, 2, 2, 19, 7, 2, 7, 3, 2, 331, 2, 179, 5, 2, 5, 3, 2, 2.  Hugo Pfoertner, Aug 27 2004
In September and November 2005, JeanLouis Charton found a(60)=54517 and a(47)=58543, respectively. Earlier, Mike Oakes found a(106)=7639 and a(124)=5839. All these large values of a(n) yield probable primes.  T. D. Noe, Dec 05 2005, Sep 18 2008
a(106) = 6529 and a(124) = 5167 are true.
a(138) through a(150) is 2,>32401,2,2,3,8839,5,7,2,3,5,271,13.  Robert Price, Feb 17 2012
Three more terms found, a(325)=81943, a(392)=64747, a(412)=56963 and also a(139)>260000, a(295)>100000, a(370)>100000, a(373)>100000. 29 unknown terms < 1000 remain.  JeanLouis Charton, Aug 15 2012
Three more terms a(577)=55117, a(588)=60089 and a(756)=96487.  JeanLouis Charton, Dec 13 2012
Three more (PRP) terms a(845)=83761, a(897)=48311, a(918)=54919.  JeanLouis Charton, Dec 20122013.
Some of the results were computed using the PrimeFormGW (PFGW) primalitytesting program.  Hugo Pfoertner, Nov 14 2019


LINKS



FORMULA



MATHEMATICA

lmt = 10000; f[n_] := Block[{p = 2}, While[p < lmt && !PrimeQ[(n+1)^p  n^p], p = NextPrime@ p]; If[p > lmt, 0, p]]; Do[ Print[{n, f[n] // Timing}], {n, 1000}] (* Robert G. Wilson v, Dec 01 2014 *)


PROG

(PARI) a(n)=forprime(p=2, default(primelimit), if(ispseudoprime((n+1)^pn^p), return(p))) \\ Charles R Greathouse IV, Feb 20 2012


CROSSREFS



KEYWORD

nonn,nice


AUTHOR



EXTENSIONS

Typo in Mathematica program corrected by Ray Chandler, Feb 22 2017


STATUS

approved



