What is the next prime with this form?

Asked Jul 29 '15 at 14:28

Active Jul 29 '15 at 15:03

Viewed 77 times

The following are primes,

$$P_1 = 2^2 + 3^3$$

$$P_2 = 2^2 + 3^3 +5^5 + 7^7$$

After these two, the only prime of such form I've found is,

$$P_3 = 2^2 + 3^3 + 5^5 + 7^7 + 11^{11} + 13^{13} +\dots+ 83^{83} + 89^{89}$$

Is there a prime number with this form after these three? (I've checked prime numbers up to 5500, but I couldn't find any others.)

edited Jul 29 '15 at 15:03

Tito Piezas III

asked Jul 29 '15 at 14:28

The Alpertron confirms that $P_3$ is indeed prime. There is a hit in the OEIS, so the question is essentially looking for the prime entries of A061789 – Tito Piezas III Jul 29 '15 at 15:07
@TitoPiezasIII, Okay thanks ( : – Freddy vs Bieber vs Jason Jul 29 '15 at 15:07
@quid, But my searching area is greater than Her. (5500 vs 1009) – Freddy vs Bieber vs Jason Jul 29 '15 at 15:17
This is not of crucial relevance in my opinion. What type of answer do you expect that could not be given to the other question? – quid Jul 29 '15 at 15:57

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