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<span style="font-family: 'Cambria">{{Divisibility|Divisibility of 31|31}}</span>;{{Infobox
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{{Infobox
 
|title = 31
 
|title = 31
 
|image = 31.png
 
|image = 31.png
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|Base-16 Form = 1F
 
|Base-16 Form = 1F
 
|previous = 29
 
|previous = 29
|next = 37
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|next = 37}}
}}
 
 
31 is a [[1-100|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. [[File:31.png|thumb]]
 
31 is a [[1-100|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. [[File:31.png|thumb]]
 
==Proofs==
 
==Proofs==
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*{{Divisibility number|No|2-30.}}
 
*{{Divisibility number|No|2-30.}}
 
*{{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==
 
===The numbers before===
 
===The numbers before===
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[[Category:Sexy Primes]]
 
[[Category:Sexy Primes]]
 
[[Category:Chen Primes]]
 
[[Category:Chen Primes]]
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[[Category:Russian-doll primes]]
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[[Category:Multiplicative Persistence 1]]

Latest revision as of 16:23, May 3, 2018

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. 
31

ProofsEdit

  • Yes — 31 can be divided by 1.
  • No — 31 cannot be divided by 2-30.
  • Yes — 31 can be divided by 31.


As an Exponent of Mersenne NumberEdit

231 - 1, which is the number 2,147,483,647, is a prime number. It is the 8th Mersenne Prime.

​Relationship with other odd numbersEdit

The numbers beforeEdit

  • 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 afterEdit

  • 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.
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