13 (just those submitted by Beedassy)

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

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 Photo credit: Patrick Kik
13 is the hypotenuse of the unique Pythagorean triangle whose area numerically equals its perimeter. [Beedassy]

The only prime subscript of a triangular number that is also a square pyramidal number : 1 + 2 + 3 + ... + 11 + 12 + 13 = 12 + 22 + 32 + 42 + 52 + 62. [Beedassy]

The prime whose square is equal to the sum of squares of all digits in which primes end: 132 = 12 + 22 + 32 + 52 + 72 + 92. [Beedassy]

The smallest prime that when concatenated to its Collatz sequence (13 --> 40 --> 20 --> 10 --> 5 --> 16 --> 8 --> 4-2-1) inexorable ending 4-2-1 forms another prime: 13421. Note that a reverse concatenation also yields a prime (12413). [Beedassy]

The smallest prime that is equidistant by a prime (3) between the sum of squares of its digits (12 + 32) and the square of the sum of its digits (1 + 3)2. [Beedassy]

In the great ancient Indian epic Mahabharata, the righteous Pandava clan, after losing their staked kingdom through deceit in a game of dice schemed out by the envious Kaurauva cousins, were forced to undergo 13 years of exile. [Beedassy]

Religious scholar A. C. Bhaktivedanta Swami Prabhupada gives the equivalent length of a yojana as approximately 13 kilometers. [Beedassy]

In chess, a Bishop controls a maximum of 13 squares of a given color. [Beedassy]

The 13 end-digits of the overwhelmingly gigantic Graham's number (g64) form a second prime concatenation: 7262464195387. [Beedassy]

(There are 12 curios for this number that have not yet been approved by an editor.)