3 = 2 + 1

5 = 2^2 + 1

7 = 2^2 + 2 + 1

11 = 2^3 + 2 + 1

13 = 2^3 + 2^2 + 1

17 = 2^4 + 1

3 + 1 = 2 * 2

3^2 + 1 = 2 * 5

3^2 + 3 + 1 = 13 = prime

3^3 + 3 + 1 = 31 = prime

3^3 + 3^2 + 1 = 37 = prime

3^4 + 1 = 2 * 41

4 + 1 = 5 = prime

4^2 + 1 = 17 = prime

4^2 + 4 + 1 = 3 * 7 ; 2^2 + 2 + 1 = 7

4^3 + 4 + 1 = 3 * 23 ; 2^3 + 2 + 1 is neither 23 nor 3.

4^3 + 4^2 + 1 = 3^4

4^4 + 1 = 257 = prime

5+1 = 2 * 3

5^2 + 1 = 2 * 13

5^2 + 5 + 1 = 31 = prime

5^3 + 5 + 1 = 131 = prime

5^3 + 5^2 + 1 = 151 = prime

6 + 1 = 7 = prime

6^2 + 1 = 37 = prime

6^2 + 6 + 1 = 43 = prime

6^3 + 6 + 1 = 223 = prime

6^3 + 6^2 + 1 = 11 * 23 ; 2^3 + 2^2 + 1 = 11

Does the prime richness extend to larger numbers, or is this an illusion

of small primes?

Kermit <

kermit@... >