# 13

This number is a prime.

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Photo credit: Patrick Kik |

The only prime subscript of a triangular number that is
also a square pyramidal number : 1 + 2 + 3 + ... + 11 + 12
+ 13 = 1^{2} + 2^{2} + 3^{2} +
4^{2} + 5^{2} + 6^{2}. [Beedassy]

The prime whose square is equal to the sum of squares of
all digits in which primes end: 13^{2} =
1^{2} + 2^{2} + 3^{2} +
5^{2} + 7^{2} + 9^{2}. [Beedassy]

The largest prime *p* such that *p* modulo
*q* is square-free for any prime *q* below
*p*. [Beedassy]

The smallest prime that when concatenated to its Collatz
sequence (__ 13__ --> 40 --> 20 -->
10 --> 5 --> 16 --> 8 -->

__) inexorable ending 4-2-1 forms another prime: 13421. Note that a reverse concatenation also yields a prime (12413). [Beedassy]__

**4-2-1**
The smallest prime that is equidistant by a prime (3)
between the sum of squares of its digits (1^{2} +
3^{2}) 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]

After needing 13 liters of blood for a major surgery during his teens, Australian James Christopher Harrison pledged to return the favour eventually becoming world record blood donor after the discovery in his blood of a unique antibody that cures Rhesus disease thereby saving millions of babies over 6 decades. [Beedassy]

The 13 end-digits of the overwhelmingly gigantic Graham's
number (*g*_{64}) form a second prime
concatenation: 7262464195387. [Beedassy]