Problems & Puzzles: Puzzles

Puzzle 492. 59 and still counting...

In certain instant of last May (09) I was momentarily 59 years old. On my request Farideh Firoozbakht sent the following puzzle:

59 is the only known multidigit number n such that sigma(n^n)+n is prime.

Next such number (if it exists) is greater than 6000 and the prime related to it, has more than 22500 digits.

1, 3 & 5 are all other known numbers n with the mentioned property.

Q1. What the prime related to n=59 in sigma(n^n)+n is?

Q2. What is the next term on 1, 3, 5, 59, ... ?





Contribution came from Jim Howell,


Jim wrote:

You will probably get the answer for part 1 from several people. The prime is:

(105 digits)


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