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The nth Prime Page will now find any of the first 2.623˙10^{15} primes or
π(x) for x up to 10^{17}. Just showing those entries submitted by 'Capelle': (Click here to show all) Levy's conjecture (1963) states that all odd numbers greater than or equal to 7 are the sum of a prime plus twice a prime. It was named after Hyman Levy, who was apparently unaware that the conjecture was first stated by Émile Lemoine in 1894. [Capelle]The smallest prime p that yields a number of the form pp when multiplied by the next prime. [Capelle] The only prime p such that (p^{2}) < ((p))^{2}. [Capelle] There are 7^{2} natural numbers n such that n is equal to the number of 7's in the decimal digits of all numbers smaller or equal to n. [Capelle] The Pollock octahedral numbers conjecture (1850) states that every number can be written as the sum of at most seven octahedral numbers. Frederick Pollock, better known as a lawyer and politician, was a contributor of papers on mathematics to the Royal Society. [Capelle] The largest known prime number that is not the sum of a triangular number, a square and a cube, all of them greater than or equal to 1. [Capelle] Seven prime numbers cannot be written as a sum of squares of primes. Note that 7 is one of them and divides their sum. [Capelle] The largest known prime number p for which the decimal expansion of p^{p} does not contain any pair of consecutive equal digits. [Capelle] There are 7 known natural numbers n such that n is the sum of two consecutive primes but not the sum of two sums of two consecutive primes. [Capelle] The number of capital letters of English alphabet with no symmetry (F, G, J, L, P, Q, R). Note that the letters P, Q and R are often used to represent the primes. [Capelle] The number of strobogrammatic capital letters of the English alphabet (H, I, N, O, S, X, Z). The word strobogrammatic begins with S, the only strobogrammatic letter with a prime index. [Capelle] Giraffes have seven neck bones, which is the same as humans and most other mammals but longer. [Capelle]
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