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|roman-number = XXXI
 
|roman-number = XXXI
 
|ordinal-number = thirty first
 
|ordinal-number = thirty first
|previous = [[29|<font color="white">29</font>]]
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|cardinal-number = thirty-one
|next = [[37|<font color="white">37</font>]]}}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]]
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|standard-form = 3.1{{E|1}}
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|Base-2 Form = 11111
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|Base-8 Form = 37
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|Base-16 Form = 1F
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|previous = 29
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|next = 37}}
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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==
*1 can divide 31
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*{{Divisibility number|Yes|1.}}
*2 cannot
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*{{Divisibility number|No|2-30.}}
*3 cannot
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*{{Divisibility number|Yes|31.}}
*4 - 28 cannot
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*29 cannot
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==As an Exponent of Mersenne Number==
*30 also cannot
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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.
*31 can divide 31
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==​Relationship with other odd numbers==
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===The numbers before===
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*The previous odd number, 29, is a prime number.
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**There are no odd numbers between 29 and 31. As a result, they are twin primes.
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*Before 29, the previous two odd numbers are 25 and 27. 25 is a square number, being 5<sup>2</sup> = 25. 27 is a cube number, being 3<sup>3</sup> = 27.
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*The prime number previous to 29 is 23.
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===The numbers after===
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*The next odd number, 33, is '''not''' a prime number. It is divisible by 3 and 11.
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*The next odd number, 35, is also '''not''' a prime number. It is divisible by 5 and 7.
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*37, the odd number following 35, is a prime number.
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**31 and 37 are six numbers apart; therefore, they are sexy primes.
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{{Navbox primes}}
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[[Category:Prime numbers from 1-100]]
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[[Category:Prime Numbers]]
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[[Category:2-Digit Prime Numbers]]
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[[Category:Twin Primes]]
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[[Category:Circular Primes]]
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[[Category:Sexy Primes]]
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[[Category:Chen Primes]]
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[[Category:Russian-doll primes]]
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[[Category:Multiplicative Persistence 1]]

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

Proofs

  • 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 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.
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