127

127
Basic Information
Cardinal Number	one hundred and twenty seven
Ordinal Number	one hundred and twenty seventh
Roman Numeral	CXXVII
Greek Numeral	ΡΚΖ´
Factorization	127
Standard Form	1.27 × 102
Different Representations
Binary Form	11111112
Ternary Form	112013
Quaternary Form	13334
Quinary Form	10025
Senary Form	3316
Septenary Form	2417
Octal Form	1778
Nonary Form	1519
Undecimal Form	10611
Duodecimal Form	A712
Tridecimal Form	9A13
Quattuordecimal Form	9114
Quindecimal Form	8715
Hexadecimal Form	7F16
Septendecimal Form	7817
Octodecimal Form	7118
Novemdecimal Form	6D19
Vigesimal Form	6720
Unvigesimal Form	6121
Duovigesimal Form	5H22
Trevigesimal Form	5C23
Quattuorvigesimal Form	5724
Quinvigesimal Form	5225
Hexavigesimal Form	4N26
Septenvigesimal Form	4J27
Octovigesimal Form	4F28
Novemvigesimal Form	4B29
Trigesimal Form	4730
Untrigesimal Form	4331
Duotrigesimal Form	3V32
Tretrigesimal Form	3S33
Quattuortrigesimal Form	3P34
Quintrigesimal Form	3M35
Hexatrigesimal Form	3J36
Previous	113
Current	127
Next	131

127 is a prime number from 101-200. 127 has 2 factors, 1 and 127. It is the 31st prime number, and the sixth prime number from 101-200. It is the largest signed 8-bit integer using two's complement.

Proofs

• — 127 is divisible by 1.

• — 127 is not divisible by 2-126.

• — 127 is divisible by 127.

Therefore, 127 is a prime number.

As an Exponent of Mersenne Number

2¹²⁷ - 1 is a prime number as well as the 12th Mersenne prime. Its decimal expansion is 170,141,183,460,469,231,731,687,303,715,884,105,727.

Relationship with other odd numbers

The numbers before

• 113 is the previous prime number.
  • The distance between 127 and 113 is 14. This is the largest gap between two consecutive prime numbers between 1 and 200.
• The prime factorization of 115 is 5 × 23.
• The prime factorization of 117 is 3² × 13.
• The prime factorization of 119 is 7 × 17.
• 121 is a square number, equal to 11².
• The prime factorization of 123 is 3 × 41.

The numbers after

• 129 is a composite number; its prime factorization is 3 × 43.
• 131 is the prime number following 127.
  • The difference between 131 and 127 is 4. Therefore, they are cousin primes.
• 133 is a composite number; its prime factorization is 7 × 19.
• 135 is a composite number; its prime factorization is 3³ × 5.
• 137 is the prime number following 131.

Trivia

• 127 is the first Friedman prime, since 127 = 2⁷ - 1. It is also the first nice Friedman prime, since 127 = -1 + 2⁷.
• 2¹²⁷ - 1 was proven to be prime in 1876 and held the record for the largest known prime number for 75 years.
• There are 127 prime numbers between 2,000 and 3,000.
• Since 129 = 127 + 2 is a semiprime, 127 is a Chen prime.
• 127 is the smallest prime number that can be expressed as the sum of two or more odd primes.
• 127 is an isolated prime, since 127 - 2 and 127 + 2 are not prime.
• 127 is the largest number with the property of being equal to 1 × prime(1) + 2 × prime(2) + 7 × prime(7), where prime(n) is the nth prime number. The only other number with this property is 43.
• 127 is the 31st prime number, meaning it is the smallest Mersenne prime with a Mersenne prime index, since 31 is a Mersenne prime. Furthermore, 127 is a super-prime, since 31 is also prime.
• 127 is the smallest prime number that the element with the atomic number is part of the extended periodic table.

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Prime Numbers 1-1,000