# 2147483647

2147483647
Cardinal two billion one hundred forty-seven million four hundred eighty-three thousand six hundred and forty-seven
Ordinal 2147483647th
(two billion one hundred forty-seven million four hundred eighty-three thousand six hundred and forty-seventh)
Factorization 2147483647
Prime Yes
Roman numeral N/A
Binary 11111111111111111111111111111112
Ternary 121121222121102021013
Quaternary 13333333333333334
Quinary 133442234340425
Senary 5530320055316
Octal 177777777778
Duodecimal 4BB2308A712
Vigesimal 1DB1F92720
Base 36 ZIK0ZJ36

The number 2,147,483,647 (two billion one hundred forty-seven million four hundred eighty-three thousand six hundred forty-seven) is the eighth Mersenne prime, equal to 231 − 1. It is one of only four known double Mersenne primes.[1]

 By 1772, Leonhard Euler had proved that 2,147,483,647 is prime.

The primality of this number was proven by Leonhard Euler, who reported the proof in a letter to Daniel Bernoulli written in 1772.[2] Euler used trial division, improving on Cataldi's method, so that at most 372 divisions were needed.[3] The number 2,147,483,647 may have remained the largest known prime until 1867.[4]

## Barlow's prediction

In 1811, Peter Barlow, not anticipating future interest in prime numbers, wrote (in An Elementary Investigation of the Theory of Numbers):

Euler ascertained that 231 − 1 = 2147483647 is a prime number; and this is the greatest at present known to be such, and, consequently, the last of the above perfect numbers [i.e., 230(231 − 1)], which depends upon this, is the greatest perfect number known at present, and probably the greatest that ever will be discovered; for as they are merely curious, without being useful, it is not likely that any person will attempt to find one beyond it.[5]

He repeated this prediction in his 1814 work A New Mathematical and Philosophical Dictionary.[6][7]

In fact a larger prime, 2127 − 1, was found in 1876 by Lucas, and in 1883 Pervushin found the prime 261 − 1.

## In computing

The number 2,147,483,647 (or hexadecimal 7FFF,FFFF16) is the maximum positive value for a 32-bit signed binary integer in computing. It is therefore the maximum value for variables declared as integers (e.g., as int) in many programming languages, and the maximum possible score, money, etc. for many video games. The appearance of the number often reflects an error, overflow condition, or missing value.[8]

The data type time_t, used on operating systems such as Unix, is a signed integer counting the number of seconds since the start of the Unix epoch (midnight UTC of 1 January 1970), and is is often implemented as a 32-bit integer.[9] The latest time that can be represented in this form is 03:14:07 UTC on Tuesday, 19 January 2038 (corresponding to 2,147,483,647 seconds since the start of the epoch). This means that systems using a 32-bit time_t type are susceptible to the Year 2038 problem.[10] (Systems employing a wider 64-bit time_t type do not suffer from this limitation.)