1. It is the smallest prime whose reverse 16 is a square.
2. It is the smaller prime such that its square can be expressed as the sum of 1, 2,3 and 4 distinct squares.
61^2 = 60^2 + 11^2
= 52^2 + 24^2 + 21^2
= 56^2 + 22^2 + 10^2 + 1^2
3. The 61st Fibonacci number (2, 504, 730, 781, 961) is the least Fibonacci number that contains all the digits from 0 to 9.
4. It is a hex number. If you have 61 coins you can arrange it into a hexagonal pattern with one coin in the middle.
5. The reciprocal of 61 = 1/61, has the decimal period of 60 which includes 6 occurrence of each of the digits 0 to 9.
1/61 = 0.0169442622950819672111---- It is the smallest reciprocal whose period has this property.
6. It is the 5th hexagonal number.
7. It is the 9th Mersenne prime exponent.
261 − 1 = 2,305,843,009,213,693,951
8. It can be expressed as the sum of squares of two consecutive numbers.
61 = 5^2 + 6^2
9. It is the 8th Keith number which moves like the Fibonacci sequence where the next term is obtained by adding the previous two terms.
6, 1, 7, 8, 15, 23, 38, 61---
10. The atomic number of Promethium is 61
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