OFFSET
1,1
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.
EXAMPLE
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
KEYWORD
nonn
AUTHOR
Jon E. Schoenfield, Dec 04 2022
STATUS
approved