The smallest number that is the sum of three cubes in two ways: 13 + 53 + 53 = 23 + 33 + 63.
In 1644, Marin Mersenne declared that 2251 - 1 was composite, but gave no proof.
An anonymous seventh grader once said "I noticed that 251, 521, and 2521 - 1 are all prime. Why don't you try 512 * 2512 - 1 or something?"
251 can be expressed using the first three primes: 23 + 35. [Sladcik]
The sum of the letters of "two hundred and fifty one" is the only self-described prime if we use the alphabet code, i.e., a = 1, b = 2, c = 3, etc. [Lundeen]
251 is the only three-digit number such that 2*251^251+1 is prime. [Opao]
The Moon not only changes phases from lunation to lunation but changes in size as the Moon moves closer to and farther away from the Earth. The length of 18 fumocies is almost exactly equal to the length of 251 lunations. [Engel]
The sum of the squares of the first three pentatopic numbers (1, 5, 15). [Silva]
Members of the Vermont 251 Club attempt to visit 251 cities and towns in the state of Vermont.
(There are 6 curios for this number that have not yet been approved by an editor.)
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