28

This number is a composite.

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

+ (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 2828 is prime. This is the largest such number less than a thousand. [Opao]

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

+ 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]

+ The current score to beat in King Kong's Prime Numbers Game. Note that 28 is a perfect number.

+ Fn2-28 is never prime, where Fn 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]

(There is one curio for this number that has not yet been approved by an editor.)

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