# 4

$t_title is "4"

$t_subtitle is "(just those submitted by Capelle)"

$t_adjust_path is "/~caldwell/curios/"

$t_class is "composite"

$nunber_id is "111"

$t_meta['description'] is "One of many pages of prime number
curiosities and trivia. This page discusses 4
Come explore a new prime today!"

Just showing those entries submitted by 'Capelle': (Click here to show all)

If we add 4 and the 4th Fibonacci number (which is prime), we find the 4th Lucas number (which is the 4th prime number). [Capelle]

If S(*n*) is the sum of the first *n* primes, then the limit of
S(2*n*)/S(*n*) = 4, as *n* approaches infinity. [Capelle]

4 is the smallest number n such that n and n! are product of factorials of primes (4 = 2!2! and 4! = 2!2!3!). [Capelle]

There are 4 known positive integers n such that the sum of all primes smaller or equal to n divides n(n+1)/2. This sum also divides the sum of all nonprimes smaller or equal to n. Note that 4 is the smallest positive integer with this property. [Capelle]

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