[ January 27, 2026 ] [ Last update [ February 1, 2026 ]
Sandwiched BEtween PRIme and SQUarE.
By Alexandru Petrescu

Here we are looking for ninedigitals and pandigitals that are sandwiched between
a prime P and a square S.

We can distinguish two cases :

P < N < S (example: N = 8; 7 < 8 < 9)
or
P > N > S (example: N = 10; 9 > 10 > 11)

The OEIS sequence of these 'beprisque' numbers is A163492

Now, Alexandru searched for N values that are nine- or pandigitals

N is a ninedigital → only one solution: N = 974251368

974251367 (prime) < 974251368 < 974251369 = 31213²

Note that 31213 is a palindrome !

N is a pandigital → two solutions: N = 5764301928 or N = 9560341728

5764301927 (prime) < 5764301928 < 5764301929 = 75923²

9560341727 (prime) < 9560341728 < 9560341729 = 97777²

[ January 30, 2026 ]

Alexandru checked also for palindromic beprisque numbers up to 10⁹

After the more trivial single digits solutions 1, 2, 3 and 8 he found

42023 (prime) < 42024 < 42025 = 205²

[ February 1, 2026 ]

Alexandru searched also for tautonymic beprisque numbers.

He sent in two solutions :

328327 (prime) < 328_328 < 328329 = 573²

528527 (prime) < 528_528 < 528529 = 727²

Note that 727 is a palindrome.
More on tautonymic numbers see my WONplate 152