7
This number is a prime.
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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
π(p2) <
(π(p))2. [Capelle]
There are 72 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 pp 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]