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The smallest number that is the sum of three cubes in two ways: 1^{3} + 5^{3} + 5^{3} = 2^{3} + 3^{3} + 6^{3}. In 1644, Marin Mersenne declared that 2^{251}  1 was composite, but gave no proof. An anonymous seventh grader once said "I noticed that 251, 521, and 2^{521}  1 are all prime. Why don't you try 512 * 2^{512}  1 or something?" 251 can be expressed using the first three primes: 2^{3} + 3^{5}. [Sladcik] The sum of the letters of "two hundred and fifty one" is the only selfdescribed prime if we use the alphabet code, i.e., a = 1, b = 2, c = 3, etc. [Lundeen] 251 is the only threedigit number such that 2*251^251+1 is prime. [Opao] The smallest of four consecutive primes in arithmetic progression (251, 257, 263, and 269). [Gallardo] 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] All the prime numbers up to 251, without repetition, appear in Benjamin Franklin's original 16by16 square. [Capelle] The sum of the squares of the first three pentatopic numbers (1, 5, 15). [Silva] Its square is the smallest number n for which the Ramanujan taufunction tau(n) is prime. It was found by D. H. Lehmer in 1965. [Capelle] Members of the Vermont 251 Club attempt to visit 251 cities and towns in the state of Vermont. Michael Jackson acquired Sony/ATV Music Publishing which owned the copyrights to 251 Beatles songs. 251 starts the first sequence of four consecutive primes containing the Beast number in their repeated differences: 6,6,6. Remember that the Horsemen of the Apocalypse are four. [Silva] The smallest prime which becomes a semiprime if any digit is deleted. [Post] The 251st Fibonacci number (F_{251}) has a sum of digits equal to 251. The two smaller prime numbers with this property are 5 and 31. [Meller] There are 251 1/4Smith numbers below 10^9. [Gupta]
(There are 12 curios for this number that have not yet been approved by an editor.)
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