Showing what's behind the curtain

Find the number of factors in an enormous factorial.

Find the 2000th hexagonal tile in which the differences between it and its 6 neighbors yield 3 primes.

The prime factorisation of binomial coefficients

Find fractions that cannot be cancelled down (resilient fraction).

Prime Subset Sums

Investigating numbers that can be expressed as the sum of a prime square, cube, and fourth power.

Investigate the Diophantine equation *x*^{2} − D*y*^{2} = 1.

Investigating which primes will never divide a repunit containing 10**n digits.

Determining the first forty prime factors of a very large repunit.

Finding composite values, n, for which n−1 is divisible by the length of the smallest repunits that divide it.