# 28

This number is a composite.

The second perfect number. Leonhard Euler (1707-1783) proved that all even
perfect numbers are of the form 2^{n-1}(2^{n} - 1), where
2^{n} - 1 is a Mersenne prime M_{n}.

(28#)^{2} ± 29 are consecutive primes. [Luhn]

28 is a perfect number expressible as the sum of first five prime numbers, i.e., 2 + 3 + 5 + 7 + 11 = 28. [Gupta]

The number of Hadamard matrices of order 28 is prime. [Rupinski]

The 28th Fibonacci number plus and minus 28 is prime, i.e., F(28)-28 and F(28)+28 are primes. [Opao]

(28!+1)/(28+1) is a prime with 28+1 digits. [Silva]

The 28th Fibonacci number plus 28^{28} is prime. This is the largest such number less than a thousand. [Opao]

28!+28^28+1 is prime. [Silva]

The product of the first twenty-eight Fibonacci numbers plus one is prime. [Schiffman]

There are 28 (a perfect number) distinct pairs of primes that sum to a thousand: (3, 997), (17, 983), (23, 977), (29, 971), (47, 953), (53, 947), (59, 941), (71, 929), (89, 911), (113, 887), (137, 863), (173, 827), (179, 821), (191, 809), (227, 773), (239, 761), (257, 743), (281, 719), (317, 683), (347, 653), (353, 647), (359, 641), (383, 617), (401, 599), (431, 569), (443, 557), (479, 521), (491, 509). [Loungrides]

F_{n}^{2}-28 is never prime, where F_{n} denotes the n-th Fibonacci number. [Poo Sung]

28 is a perfect number expressible as the sum of first five nonprime numbers, i.e., 1 + 4 + 6 + 8 + 9 = 28. [Gaydos]

The only known number which can be expressed as the sum of the first non-negative integers (1 + 2 + 3 + 4 + 5 + 6 + 7), the first primes (2 + 3 + 5 + 7 + 11) and the first non-primes (1 + 4 + 6 + 8 + 9). There is probably no other number with this property. [Bourcereau]

There are 28 prime numbers with distinct digits that are each the sum of the first n primes. The largest is 906437281 which is the sum of the first 13306 primes. [Gaydos]

28 is a semiprime. [Abbott and Costello]

The sum of the first 28 Keith numbers is a prime number. Note that 28 is the only known Keith number making the previous statement true. [Honaker]