Changes: 31

Latest revision as of 14:24, 29 November 2023

31

Basic Information

Cardinal Number

thirty-one

Ordinal Number

thirty first

Roman Numeral

XXXI

Greek Numeral

ΛΑ´

Factorization

31

Standard Form

3.1 × 10¹

Different Representations

Binary Form

11111₂

Ternary Form

1011₃

Quaternary Form

133₄

Quinary Form

111₅

Senary Form

51₆

Septenary Form

43₇

Octal Form

37₈

Nonary Form

34₉

Undecimal Form

29₁₁

Duodecimal Form

27₁₂

Tridecimal Form

25₁₃

Quattuordecimal Form

23₁₄

Quindecimal Form

21₁₅

Hexadecimal Form

1F₁₆

Septendecimal Form

1E₁₇

Octodecimal Form

1D₁₈

Novemdecimal Form

1C₁₉

Vigesimal Form

1B₂₀

Unvigesimal Form

1A₂₁

Duovigesimal Form

19₂₂

Trevigesimal Form

18₂₃

Quattuorvigesimal Form

17₂₄

Quinvigesimal Form

16₂₅

Hexavigesimal Form

15₂₆

Septenvigesimal Form

14₂₇

Octovigesimal Form

13₂₈

Novemvigesimal Form

12₂₉

Trigesimal Form

11₃₀

Untrigesimal Form

10₃₁

Duotrigesimal Form

V₃₂

Tretrigesimal Form

V₃₃

Quattuortrigesimal Form

V₃₄

Quintrigesimal Form

V₃₅

Hexatrigesimal Form

V₃₆

Previous	Current	Next
29	31	37

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

— 31 can be divided by 1.

— 31 cannot be divided by 2-30.

— 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.

Prime Numbers 1-1,000

1-100
1-25	2 • 3 • 5 • 7 • 11 • 13 • 17 • 19 • 23
26-50	29 • 31 • 37 • 41 • 43 • 47
51-75	53 • 59 • 61 • 67 • 71 • 73
76-100	79 • 83 • 89 • 97

101-200
101-125	101 • 103 • 107 • 109 • 113
126-150	127 • 131 • 137 • 139 • 149
151-175	151 • 157 • 163 • 167 • 173
176-200	179 • 181 • 191 • 193 • 197 • 199

201-400
201-250	211 • 223 • 227 • 229 • 233 • 239 • 241
250-300	251 • 257 • 263 • 269 • 271 • 277 • 281 • 283 • 293
301-350	307 • 311 • 313 • 317 • 331 • 337 • 347 • 349
351-400	353 • 359 • 367 • 373 • 379 • 383 • 389 • 397

401-600
401-450	401 • 409 • 419 • 421 • 431 • 433 • 439 • 443 • 449
450-500	457 • 461 • 463 • 467 • 479 • 487 • 491 • 499
501-550	503 • 509 • 521 • 523 • 541 • 547
551-600	557 • 563 • 569 • 571 • 577 • 587 • 593 • 599

601-800
601-650	601 • 607 • 613 • 617 • 619 • 631 • 641 • 643 • 647
651-700	653 • 659 • 661 • 673 • 677 • 683 • 691
701-750	701 • 709 • 719 • 727 • 733 • 739 • 743
751-800	751 • 757 • 761 • 769 • 773 • 787 • 797

801-1,000
801-850	809 • 811 • 821 • 823 • 827 • 829 • 839
851-900	853 • 857 • 859 • 863 • 877 • 881 • 883 • 887
901-950	907 • 911 • 919 • 929 • 937 • 941 • 947
951-1000	953 • 967 • 971 • 977 • 983 • 991 • 997

@@ Line 1: / Line 1: @@
 {{Infobox
 |title = 31
-|image = 31.png
+|image = 31-D.png
 |imagewidth = 200
 |roman-number = XXXI
 |ordinal-number = thirty first
+|cardinal-number = thirty-one
-|previous = [[29|<font color="white">29</font>]]
+|standard-form = 3.1{{E|1}}
-|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]]
+|Base-2 Form = 11111
+|Base-8 Form = 37
+|Base-16 Form = 1F
+|previous = 29
+|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-D.png|thumb]]
+It is also the second pi-prime (First is [[3]]).
 ==Proofs==
+*{{Divisibility number|Yes|1.}}
-*1 can divide 31
+*{{Divisibility number|No|2-30.}}
-*2 cannot
+*{{Divisibility number|Yes|31.}}
-*3 cannot
-*4 - 28 cannot
+==As an Exponent of Mersenne Number==
-*29 cannot
+<sup>31</sup> - 1, which is the number 2,147,483,647, is a prime number. It is the 8th Mersenne Prime.
-*30 also cannot
-*31 can divide 31
+==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 5<sup>2</sup> = 25. 27 is a cube number, being 3<sup>3</sup> = 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.
+{{Navbox primes}}
+[[Category:Prime numbers from 1-100]]
+[[Category:Prime Numbers]]
+[[Category:2-Digit Prime Numbers]]
+[[Category:Twin Primes]]
+[[Category:Circular Primes]]
+[[Category:Sexy Primes]]
+[[Category:Chen Primes]]
+[[Category:Russian-doll primes]]
+[[Category:Multiplicative Persistence 1]]
+[[Category:Pi-Primes]]
+[[Category:Mersenne Primes]]
+[[Category:Primes of the Form Floor]]
+[[Category:Iccanobif Primes]]
+[[Category:Emirps]]
+[[Category:Right-truncatable Primes]]
+[[Category:Super Primes]]
+[[Category:Centered Triangular Primes]]
+[[Category:Centered Decagonal Primes]]