Showing what's behind the curtain

Find a set of five primes for which any two primes concatenate to produce another prime.

Find the sum of the only set of six 4-digit figurate numbers with a cyclic property.

Find the smallest cube for which exactly five permutations of its digits are cube.

Count how many n-digit positive integers exist which are also an nth power.

Find the continued fractions for N ≤ 10000 have an odd period.

Find the sum of digits in the numerator of the 100th convergent of the continued fraction for *e*.

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

Find the maximum total from top to bottom in a large triangle of numbers using an efficient algorithm.

Find the maximum 16-digit string for a “magic” 5-gon ring.

Find the value of n ≤ 1,000,000 for which n/φ(n) is a maximum.