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{{Infobox |
{{Infobox |
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|title = 31 |
|title = 31 |
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− | |image = 31.png |
+ | |image = 31-D.png |
|imagewidth = 200 |
|imagewidth = 200 |
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|roman-number = XXXI |
|roman-number = XXXI |
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|Base-16 Form = 1F |
|Base-16 Form = 1F |
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|previous = 29 |
|previous = 29 |
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⚫ | |||
− | |next = 37}} |
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+ | |||
⚫ | |||
+ | It is also the second pi-prime (First is [[3]]). |
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+ | |||
==Proofs== |
==Proofs== |
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*{{Divisibility number|Yes|1.}} |
*{{Divisibility number|Yes|1.}} |
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*{{Divisibility number|No|2-30.}} |
*{{Divisibility number|No|2-30.}} |
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*{{Divisibility number|Yes|31.}} |
*{{Divisibility number|Yes|31.}} |
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+ | |||
+ | ==As an Exponent of Mersenne Number== |
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+ | 2<sup>31</sup> - 1, which is the number 2,147,483,647, is a prime number. It is the 8th Mersenne Prime. |
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+ | |||
==Relationship with other odd numbers== |
==Relationship with other odd numbers== |
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===The numbers before=== |
===The numbers before=== |
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[[Category:Chen Primes]] |
[[Category:Chen Primes]] |
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[[Category:Russian-doll primes]] |
[[Category:Russian-doll primes]] |
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+ | [[Category:Multiplicative Persistence 1]] |
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+ | [[Category:Pi-Primes]] |
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+ | [[Category:Mersenne Primes]] |
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+ | [[Category:Primes of the Form Floor]] |
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+ | [[Category:Iccanobif Primes]] |
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+ | [[Category:Emirps]] |
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+ | [[Category:Right-truncatable Primes]] |
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+ | [[Category:Super Primes]] |
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+ | [[Category:Centered Triangular Primes]] |
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+ | [[Category:Centered Decagonal Primes]] |
Latest revision as of 14:24, 29 November 2023
31 is a prime number from 1-100. 31 has 2 factors, 1 and 31. It is said to be a number wherein when digits are added together, they make a composite number. It is the eleventh prime number, and the eleventh prime number from 1-100.
It is also the second pi-prime (First is 3).
Proofs
As an Exponent of Mersenne Number
231 - 1, which is the number 2,147,483,647, is a prime number. It is the 8th Mersenne Prime.
Relationship with other odd numbers
The numbers before
- The previous odd number, 29, is a prime number.
- There are no odd numbers between 29 and 31. As a result, they are twin primes.
- Before 29, the previous two odd numbers are 25 and 27. 25 is a square number, being 52 = 25. 27 is a cube number, being 33 = 27.
- The prime number previous to 29 is 23.
The numbers after
- The next odd number, 33, is not a prime number. It is divisible by 3 and 11.
- The next odd number, 35, is also not a prime number. It is divisible by 5 and 7.
- 37, the odd number following 35, is a prime number.
- 31 and 37 are six numbers apart; therefore, they are sexy primes.