Prime numbers of the form $P^Q+R^S$

Question

Is there a prime number of the form $P^Q+R^S$ where $P,Q,R,S$ are four distinct prime numbers?

Examples: $2^3+7^5$, $2^3+5^{11}$ are not primes, $2^5+11^7$ is not a prime.

In any case, you need absolutely to use the prime $2$... – Martigan Jun 15 '15 at 15:13 — Martigan, Jun 15 '15 at 15:13
@Martigan yasman of course – karra zanny Jun 15 '15 at 15:13 — karra zanny, Jun 15 '15 at 15:13
2^3+11^5=161059 http://www.wolframalpha.com/input/?i=161059 – Exodd Jun 15 '15 at 15:14 — Exodd, Jun 15 '15 at 15:14
@Exodd yes that is correct,are there the others – karra zanny Jun 15 '15 at 15:18 — karra zanny, Jun 15 '15 at 15:18

Dietrich Burde · Accepted Answer · 2015-06-15T15:25:13.730

1

Yes, there are many solutions, e.g., $2^7+3^{13}=1594451 $ is prime. Further solutions are $2^{11}+3^{29}=6863037736693$ and $2^5+3^{23}=94143178859$.

edited Jun 15 '15 at 15:25

answered Jun 15 '15 at 15:14

Dietrich Burde

130,978

Prime numbers of the form $P^Q+R^S$

1 Answers1