A100856 -id:A100856

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A100858

Primes of the form (p - 1)! + p, p prime.

+10
13

3, 5, 29, 727, 3628811, 80658175170943878571660636856403766975289505440883277824000000000053

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

a(n) = A100856(k) = A100857(k) for some k.

Subset of A073309. - R. J. Mathar, Sep 02 2008

No more terms for p < 1250. - Vincenzo Librandi, Dec 26 2010

LINKS

Table of n, a(n) for n=1..6.

PROG

(Magma)[ a: p in PrimesUpTo(250) | IsPrime(a) where a is Factorial(p-1)+p ]; // Vincenzo Librandi, Dec 26 2010

CROSSREFS

Cf. A092791.

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Nov 20 2004

STATUS

approved

A100857

a(n) = greatest prime factor of (prime(n) - 1)! + prime(n).

+10
3

3, 5, 29, 727, 3628811, 6599, 6385271, 1291883, 315389197, 123662437024088191, 2107707330310062524424576119, 50717732086848522419, 14602944428087660261, 55353784249983832172137, 16166897314580017

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..24 (using factordb.com)

Dario A. Alpern, Factorization using the Elliptic Curve Method.

FactorDB, Status of 97+96!.

FORMULA

a(n) = A006530(A100856(n)).

a(n) > A000040(n).

EXAMPLE

n=6: (prime(6)-1)! + prime(6) = 12! + 13 = 479001600 + 13 = 479001613 = 29*2503*6599, therefore a(6) = 6599.

MATHEMATICA

FactorInteger[(#-1)!+#][[-1, 1]]&/@Prime[Range[15]] (* Harvey P. Dale, Jul 23 2011 *)