[ November 11, 2006 ]
Two nice consecutive primes
by Farideh Firoozbakht (email)
I found two nice consecutive primes p & q
related to the palindromic number 1551.
p = n^n – (n – 1) and q = n^n + (n – 1)
or
p = 1551^{1551} – (1551 – 1) and q = 1551^{1551} + (1551 – 1)
or
p = 1551^{1551} – 1550 and q = 1551^{1551} + 1550

The next term (q) of A058912 is thus 1551.
I sent a similar email to Giovanni Resta and
he checked the primality of p & q with pfgw.
He wrote: " They are very nice indeed !
It was so difficult to believe in such a coincidence,
with numbers of 4949 digits, that I must confess
that I checked them with pfgw ! "