A243100 Primes of the form x^(y+1)-y^x, for x,y > 0.

3, 7, 19, 179, 543607, 129136067, 94143168179, 11920928949924493, 36472996377170722403, 61159026180004467059, 1341068619659378429383, 10301051460877537453973547005699, 710542735760100185871124061615149, 17763568394002504646778106434649157

Offset: 1

Author

M. F. Hasler, Aug 19 2014

Keywords

• nonn

Comments

See A123206 for primes of the form x^y-y^x with x,y>1. If y=1 is allowed, any prime p is obtained for x=p+1; this motivates the "y+1" in the exponent of the present sequence.

See also A086877 (and A098463) for primes of the form (x+1)^x-x^x.

y=0 would give "Primes of the form x", so y>0 is required. y=1 gives x^2-1 = (x-1)*(x+1) which is only prime for x=2. - Jens Kruse Andersen, Aug 23 2014

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 1..59
• J. S. Gerasimov, x^(y + 1) - y^x, SeqFan list, Aug 18, 2014

Crossrefs

See also A072164.

Programs

PARI

a=[];for(S=1,199,for(x=1,S-1,ispseudoprime(p=x^(1+y=S-x)-y^x)&&a=concat(a,p)));vecsort(a) \\ The list calculated this way is probably not complete up to the last terms. E.g., a 46 digit prime is found for x=3, y=97 after three larger terms for smaller S=x+y.

PARI

m=300; a=[]; for(x=1, m+5, for(y=1, m+5, p=x^(y+1)-y^x; if(p<2^m && ispseudoprime(p), a=concat(a, p)))); a=vecsort(a) \\ Compute all terms below 2^m. Jens Kruse Andersen, Aug 23 2014