In order to try and add to the integer sequence at http://oeis.org/A173795 I am attempting to fill in a 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:
- Are 4417190430889897 and 84658174289284249 the smallest primes for n=11 and 12 respectively?
- Is 107122676734733201 the smallest prime where n=14?
- Is there a known prime < 107122676734733201 where n=13?