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# 613

NASA used the space shuttle to place the Hubble Space Telescope (HST) in orbit around Earth at an altitude of 613 kilometers. [Luhn]

6+1+3 = 10, corresponding to the Ten Commandments. 613 is the 13th prime number whose digits add up to 10. Note the 13 Jewish principles of belief. [Doneel]

There are exactly 613 precepts (or laws) within the five books of Moses. [Aaron]

Even though only 6 of the 13 volumes of his *Arithmetica* have survived, Diophantus was regarged as the "Father of Algebra." [Motz]

The 18th centered square number. Note that 18 = 6*1*3. [Post]

NGC 613 is a barred spiral galaxy in the southern constellation Sculptor. The sum of digits of 613 approximates its visual magnitude.

613 is a mathematical enigma in the bewildering story *Number of the End* by Jason Earls. "Bring the first digit back to get 136, it's triangular. Now bring the first digit of that back to get 361, it's a square."

613^{2} is the largest known square that divides a number of
the form n!+1, which happens when n=229, another prime. [Noe]

The only 3-digit number p such that 3^p-R(p) is prime. [Loungrides]

Smallest prime in the first prime triple whose the terms remain prime when each digit is replaced by its cube: (613, 216127), (617, 2161343), (619, 2161729). [Loungrides]

The smallest prime in a set of eleven consecutive primes such that deleting the first digit we find another set of eleven distinct primes. [Loungrides]

The only 3-digit prime formed from the index of a prime p followed by p, i.e., the 6th prime is 13. [Loungrides]

The B-F bond energy is close to 613 kJ/mol. [Yoder]