137 (number)
natural number
137 (one hundred [and] thirty-seven) is the natural number following 136 and preceding 138.
Mathematics
137 is:
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
{\displaystyle 3n-1}
.
the fourth Stern prime.
a Pythagorean prime: a prime number of the form
4
n
+
1
{\displaystyle 4n+1}
, where
n
=
34
{\displaystyle n=34}
(
137
=
4
×
34
+
1
{\displaystyle 137=4\times 34+1}
) or the sum of two squares
11
2
+
4
2
=
(
121
+
16
)
{\displaystyle 11^{2}+4^{2}=(121+16)}
.
a combination of three terms
4
3
+
3
4
−
2
3
=
(
64
+
81
−
8
)
{\displaystyle 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).
In decimal notation, 1/137 = 0.007 299 27, 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.
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