137 (number) explained

Number:	137
Factorization:	prime
Prime:	33rd
Divisor:	1, 137

137 (one hundred [and] thirty-seven) is the natural number following 136 and preceding 138.

Mathematics

• the 33rd prime number; the next is 139, with which it comprises a twin prime, and thus 137 is a Chen prime.
• an Eisenstein prime with no imaginary part and a real part of the form

3 n - 1 .

• the fourth Stern prime.
• a Pythagorean prime: a prime number of the form

4 n +1 , where n =34  (137=4 x 34+1 ) or the sum of two squares 11 ^{2} +4 ^{2} = ( 121+16 ) .

• a combination of three terms

4 ^{3} +3 ^{4} -2 ^{3} = ( 64+81-8 ) , cube of 4 + Triangular number T4+T2 on each cube face (along 3 axes) - peaks (single 6th peak as free link)

• a strong prime in the sense that it is more than the arithmetic mean of its two neighboring primes.
• a strictly non-palindromic number and a primeval number.
• a factor of 10001 (the other being 73) and the repdigit 11111111 (= 10001 × 1111).
• using two radii to divide a circle according to the golden ratio yields sectors of approximately 137.51° (the golden angle) and 222° in degree system so 137 is the largest integer before it.
• In decimal notation, 1/137 = 0., so its period value happens to be palindromic and has a period length of only 8. However, this is only special to decimal, as in pentadecimal it (1/92) has a period length of twenty-four (24) and the period value is not at all palindromic.