A358879 Primes p such that p^2 + 1 has more divisors than p^2 - 1.

2917, 5443, 7187, 9133, 10357, 12227, 12967, 13043, 14243, 17047, 20507, 20743, 21767, 25657, 27893, 27997, 28163, 30307, 32323, 32443, 33493, 33623, 34157, 34367, 34897, 35537, 37783, 37957, 39827, 41387, 41893, 42793, 43633, 44357, 49109, 49993, 56597, 56857

Offset: 1

Author

Jon E. Schoenfield, Dec 04 2022

Keywords

• nonn

Comments

Fewer than 1.2% of the first million primes have this property.

For all primes p > 3, p^2 - 1 is divisible by 24 (since it is factorable as (p-1)*(p+1)), but p^2 + 1, although it is even, is divisible by neither 4 nor 3.

Examples

			2917 is a term:
2917^2 - 1 = 8508888 = 2^3 * 3^6 * 1459 has 56 divisors, but
2917^2 + 1 = 8508890 = 2 * 5 * 13 * 29 * 37 * 61 has 64.
399173 is a term:
399173^2 - 1 = 159339083928 = 2^3 * 3 * 66529 * 99793 has 32 divisors, but
399173^2 + 1 = 159339083930 = 2 * 5 * 13 * 17 * 29 * 53 * 61 * 769 has 256.
		

Crossrefs

Cf. A000005, A000040, A341655, A341658, A341660.