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GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits)

+ The magic constant in the only possible magic hexagon (which utilizes all the natural integers up to and including the prime number 19).

+ The sum of squares of the first three primes (22 + 32 + 52). [Kimberling]

+ The number of Mersenne primes known to humanity prior to the 21st century.

+ The sum of the first 38 cubed primes (23 + 33 + ... + 1633) is prime. [De Geest]

+ 38 = 2 * 19. Note that 32 + 819 is prime. [Honaker]

+ 38 * 238 + 38 + 1 is prime. [Noll]

+ 38 of the first one hundred primes are full period primes. Note that it is conjectured that about 3/8 of all primes are full period primes.

+ The largest known even number which can be represented as sum of two distinct primes in only one way (i.e., 38 = 31 + 7). [Gupta]

+ Let spf = sum of prime factors (where spf(p) = 0); then spf(38) = 21, spf(21) = 10, spf(10) = 7, and spf(7) = 0. Note that 21 + 10 + 7 + 0 = 38. The numbers 20 and 74 also share this property. [Moseley]

+ 38 = 3(pi(3)) + 8(pi(8)). [Firoozbakht]

+ The largest even number such that every partition into two odd parts contains at least one prime. [Brahinsky]

+ 38 is the average of first primes up to 83. [Silva]

(There are 3 curios for this number that have not yet been approved by an editor.)

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