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# 2267

This number is a prime.

The smallest four-digit zeroless prime such that 2+267, 22+67, and 226+7 are also distinct primes. [Opao]

2267 is the sum of the squares of three distinct primes (3^2 + 7^2 + 47^2). [Suzuki]

The only prime less than a googol of form p^a-(q^b+r^c) where (p, q, r) are three successive primes p > q > r and a, b, c their orders, i.e., 7^4-(5^3+3^2). [Loungrides]

(2267, 2269) is the first pair of twin primes of form (n*R(n)-1, n*R(n)+1), case n=36. Can you find the next one such pair? [Loungrides]

There are 2267 prime numbers that have distinct digits in both octal and hexadecimal notation. The largest is 2050571. [Gaydos]

(There is one curio for this number that has not yet been approved by an editor.)

Printed from the PrimePages <t5k.org> © G. L. Honaker and Chris K. Caldwell