  61 (sixty-one) is the natural number following 60 and preceding 62.  ==in mathematics== it is the 18th prime number. the previous is 59, with which it comprises a twin prime. sixty-one is a cuban prime of the form p = (x^3 - y^3) / (x - y), x = y + 1. sixty-one is the smallest proper prime, a prime p which ends in the digit 1in base 10 and whose reciprocal in base 10 has a repeating sequence with length p-1. in such primes, each digit 0, 1, ..., 9 appears in the repeating sequence the same number of times as does each other digit (namely, (p-1)/10 times).dickson, l. e., history of the theory of numbers, volume 1, chelsea publishing co., 1952. 61 is 9th mersenne prime exponent. (261 â 1 = ) sixty-one is the sum of two squares, 52 + 62, and it is also a centered square number, a centered hexagonal number and a centered decagonal number. it is the sixth euler zigzag number (or up/down number). in base 14, 61 is a unique prime since no other prime has a 6-digit period in base 14. since 8! + 1 is divisible by 61 but 61 is not one more than a multiple of 8, 61 is a pillai prime. in the list of fortunate numbers, 61 occurs thrice, since adding 61 to either the tenth, twelfth or seventeenth primorial gives a prime number (namely 6,469,693,291; 7,420,738,134,871; and 1,922,760,350,154,212,639,131). it is also a keith number, because it recurs in a fibonacci-like sequence started from its base 10 digits: 6, 1, 7, 8, 15, 23, 38, 61... ==in science== * the chemical element with the atomic number 61 (promethium), a lanthanide, is the element with the secondary lowest ordinal number that does not possess any stable isotopes. the promethium preceding element with atomic number 60 (neodymium) and the promethium following element 62 (samarium) have all stable isotopes. ===astronomy=== *messier object m61, a magnitude 10.5 galaxy in the constellation virgo *the new general catalogue object ngc 61, a double spiral galaxy in the constellation pisces *the saros number of the solar eclipse series which began on -973 may 10 and ended on 289 june 5. the duration of saros series 61 was 1262.1 years, and it contained 71 solar eclipses. *the saros number of the lunar eclipse series which began on -870 october 20 and ended on 609 march 26. the 
Integers