show/hide this revision's text 4 Grammar edited.

In order to try and add to the integer sequence at http://oeis.org/A173795 I am attempting to fill in a missing gap in a sequence of primes that are the sum of a positive cube and a square in n different ways.

To date, and as far as I am aware, for n=0 to 10 the smallest primes are known that fulfill this criteria. The largest being 333413867957257 where n = 10.

Candidates for the smallest at n=11 and n=12 are due to Elkies and these are 4417190430889897 and 84658174289284249 respectively.

There then exists a gap at n=13 before 107122676734733201 fulfills the criteria for n=14.

My questions are:

  1. Are 4417190430889897 and 84658174289284249 the smallest primes for n=11 and 12 respectively?
  2. Is 107122676734733201 the smallest prime where n=14?
  3. Is there a known prime < 107122676734733201 where n=13?

Kevin.
show/hide this revision's text 3 Clarified question slightly, again.

In order to try and add to the integer sequence at http://oeis.org/A173795 I am attempting to fill in a missing gap in a sequence of primes that are sums the sum of a positive cubes cube and squares a square in n different ways.

To date, and as far as I am aware, for n=0 to 10 the smallest primes are known that fulfill this criteria. The largest being 333413867957257 where n = 10.

Candidates for the smallest at n=11 and n=12 are due to Elkies and these are 4417190430889897 and 84658174289284249 respectively.

There then exists a gap at n=13 before 107122676734733201 fulfills the criteria for n=14.

My questions are:

  1. Are 4417190430889897 and 84658174289284249 the smallest primes for n=11 and 12 respectively?
  2. Is 107122676734733201 the smallest prime where n=14?
  3. Is there a known prime < 107122676734733201 where n=13?

Kevin.
show/hide this revision's text 2 Added OEIS reference

I'm trying

In order to try and add to the integer sequence at http://oeis.org/A173795 I am attempting to fill in a missing gap in a sequence of primes that are sums of positive cubes and squares in n different ways.

To date, and as far as I am aware, for n=0 to 10 the smallest primes are known that fulfill this criteria. The largest being 333413867957257 where n = 10.

Candidates for the smallest at n=11 and n=12 are due to Elkies and these are 4417190430889897 and 84658174289284249 respectively.

There then exists a gap at n=13 before 107122676734733201 fulfills the criteria for n=14.

My questions are:

  1. Are 4417190430889897 and 84658174289284249 the smallest primes for n=11 and 12 respectively?
  2. Is 107122676734733201 the smallest prime where n=14?
  3. Is there a known prime < 107122676734733201 where n=13?

Kevin.
show/hide this revision's text 1