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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) Just showing those entries submitted by 'Capelle': (Click here to show all) The smallest odd prime equal to the sum of two squares and to the arithmetic mean of two squares. [Capelle]There are 5 families of butterflies. [Capelle] The number of known strobogrammatic squares. The number of distinct digits to write them. [Capelle] The largest Pell number (coincidentally prime) of the form x^{2} + 1. Note that 5 = 2^{2} + 1, where 1 and 2 are the two other Pell numbers of this form. [Capelle] The only prime of the form 4^{n} + n^{4}, where n is a positive integer. [Capelle] Every positive integer can be written as the sum of 5 pentagonal numbers. Note that 5 is the only prime pentagonal number. [Capelle] The only known prime p such that sigma(p) divides sigma(sigma(p)). [Capelle] The only prime p such that phi(p) = tau(p) + 2, phi(p) = tau(p) * 2, and phi(p) = tau(p)^{2}. [Capelle] The largest known prime p such that fib(p) divides p!, but the only prime equal to fib(p). [Capelle] There are 5 natural numbers n such that n is equal to the number of 5's in the decimal digits of all natural numbers smaller or equal to n. [Capelle] Pollock's conjecture (1850) states that every number can be written as the sum of at most five tetrahedral numbers. No connection with the famous painting No. 5, 1948, by Jackson Pollock. [Capelle] The largest known prime number p such that binomial(2p,p) is cubefree. [Capelle]
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