A page of the Numeropedia - the Special Encyclopedia of Numbers
[Math.] Sum of the first 224 cube numbers:
13+23+…+2243 = 635,040,000 = (1+2+…+224)2 = 25,2002.
[Math.] The smallest number that is the sum of two 4th powers in 2 ways: 635,318,657 = 594+1584 = 1334+1344.
[Math.] The infinite sum Sn(1/n12) = p12×691/638512875 = Z(12), where n runs over all positive integers and Z(s) is the Riemann zeta function over complex variable s.
[Math.] 638,523,2494 = 630,662,6244+275,156,2404+219,076,4654. (Allan MacLeod, 1997)
[Math.] 252792 = 639,027,841, a square using all 9 digits 0-9 once, except digit 5.
[Math.] For any xyz = 100 to 999, there are always six 6-digit numbers abc,edf such that the sum (xyz+abc,def) is equal to one of 6 digit-rotations of 142,857 and the number xyz,abc,def is a multiple of 142,857.
For any xyz = 100 to 999, there are always twelve 6-digit numbers abc,edf such that the sum (xyz+abc,def) is equal to one of 12 digit-rotations of 076,923 or 153,846 and the number xyz,abc,def is a multiple of 76,923.