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(just those submitted by Capelle)
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GIMPS has discovered a new largest known prime number: 282589933-1 (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 x2 + 1. Note that 5 = 22 + 1, where 1 and 2 are the two other Pell numbers of this form. [Capelle]

+ The only prime of the form 4n + n4, 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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