2,147,483,647
2,147,483,647 is 2³¹ − 1: the largest value a signed 32-bit integer can hold, and the eighth Mersenne prime.
- Odd
- Prime
Where 2,147,483,647 fits
Why 2,147,483,647 is special
It is famous twice over for reasons that have nothing to do with each other. Euler proved it prime in 1772 and it stayed the largest known prime for nearly a century. Unconnectedly, two's-complement arithmetic makes it the ceiling of a signed 32-bit integer, which is why so many unrelated systems fail at exactly the same number — and why 32-bit Unix time runs out in 2038.
2,147,483,647 connects to:
- processor and software bit widths — appears in
- 2038 — is associated with
Same number, different meanings
How 2,147,483,647 is understood across different contexts — never implying one meaning because of another.
- Mathematics
It is famous twice over for reasons that have nothing to do with each other. Euler proved it prime in 1772 and it stayed the largest known prime for nearly a century. Unconnectedly, two's-complement arithmetic makes it the ceiling of a signed 32-bit integer, which is why so many unrelated systems fail at exactly the same number — and why 32-bit Unix time runs out in 2038.
- Technology & computing
Two's-complement representation splits a 32-bit field into 2,147,483,648 negative values and 2,147,483,647 positive ones, so this is the largest signed 32-bit integer. Systems built independently of one another therefore fail at exactly the same number, which is why the value is recognisable to people who have never deliberately looked it up.
- History
2,147,483,647 is the eighth Mersenne prime, 2³¹ − 1. Euler established its primality in 1772, and it remained the largest known prime until 1867. That it is also the signed 32-bit ceiling is a coincidence of the same exponent, not a connection between the two facts.
- Media & popular culture
In 2014 YouTube moved its view counter to a 64-bit integer after the most-watched video at the time approached 2,147,483,647 views. It is the clearest public example of the ceiling being reached by ordinary growth rather than by a bug.
Not just a mathematical number
2,147,483,647is also used in ways where ordinary arithmetic doesn't apply — each listed below with what genuinely does and doesn't follow from it.
- Mathematical number
A genuine quantity — its mathematical properties (prime, square, factors, and so on) are real facts about it.
A genuine quantity that ordinary arithmetic applies to — it can be prime, even, a perfect square, added to another number meaningfully, and so on.
- Measurement
Also used as a measurement — Processor and software bit-widths.
A quantity expressed against a defined unit or standard (24 hours in a day, 60 seconds in a minute) — arithmetic is meaningful, but the specific value is a fixed convention of the measuring system, not a discovered mathematical property.
2,147,483,647 is part of
Factors & digit properties
- Divisors (2)
- 1, 2147483647
- Prime factorisation
- 2147483647
- Digit sum
- 46
- Digital root
- 1
Representations
- Decimal
- 2147483647
- Scientific notation
- 2.147 × 10^9
Roman numerals
Roman numerals as modelled here goes up to 3,999.
Binary
Binary (base 2) as modelled here goes up to 1,000,000,000.
Octal
Octal (base 8) as modelled here goes up to 1,000,000,000.
Hexadecimal
Hexadecimal (base 16) as modelled here goes up to 1,000,000,000.
Other mathematical patterns
- Deficient number
- Mersenne prime
Related numbers & connections
2³¹ − 1 is the largest signed value a 32-bit field holds, which is what makes it the shared failure point of otherwise unrelated systems.
32-bit Unix time reaches 2,147,483,647 seconds at 03:14:07 UTC on 19 January 2038 and overflows.
View 2038 →Numbers Around Us
- appears inProcessor and software bit-widths
why?
Strength 0.50, confidence "high".
Other connections
- is associated with2038
why?
Strength 0.50, confidence "high".
Technology & computing
Two's-complement representation splits a 32-bit field into 2,147,483,648 negative values and 2,147,483,647 positive ones, so this is the largest signed 32-bit integer. Systems built independently of one another therefore fail at exactly the same number, which is why the value is recognisable to people who have never deliberately looked it up.
DocumentedTechnology & computingUnix time counts seconds from 1 January 1970. Held in a signed 32-bit integer it reaches 2,147,483,647 at 03:14:07 UTC on 19 January 2038 and overflows. The fix — a 64-bit time type — is well understood and widely deployed; the difficulty is embedded and long-lived systems that are hard to reach rather than any doubt about what to do.
DocumentedTechnology & computing
History
2,147,483,647 is the eighth Mersenne prime, 2³¹ − 1. Euler established its primality in 1772, and it remained the largest known prime until 1867. That it is also the signed 32-bit ceiling is a coincidence of the same exponent, not a connection between the two facts.
DocumentedHistory
Mathematics
A Mersenne number 2ⁿ − 1 can only be prime when n is itself prime, which is why the search for large primes has concentrated on this form for centuries. 31 is prime, so 2³¹ − 1 is a candidate; the converse fails, and 2¹¹ − 1 = 23 × 89 is the standard counterexample.
DocumentedMathematics
Media & popular culture
In 2014 YouTube moved its view counter to a 64-bit integer after the most-watched video at the time approached 2,147,483,647 views. It is the clearest public example of the ceiling being reached by ordinary growth rather than by a bug.
DocumentedMedia & popular culture
Common questions
Why is 2147483647 the maximum integer?
It is the maximum for a *signed 32-bit* integer specifically. Two's complement splits 2³² possible values into 2,147,483,648 negative ones and 2,147,483,647 positive ones, with zero taking the remaining slot. Wider types have much larger maxima; this one is memorable because 32 bits was the default for so long.
What happens in 2038?
Unix time counts seconds since 1 January 1970, and in a signed 32-bit integer it reaches 2,147,483,647 at 03:14:07 UTC on 19 January 2038, then overflows to a negative number. The fix — a 64-bit time type — is well understood and widely deployed. The hard part is embedded systems that are difficult to reach, not any uncertainty about what to do.
Is 2147483647 a prime number?
Yes. It is the eighth Mersenne prime, 2³¹ − 1, proved prime by Euler in 1772, and it remained the largest known prime until 1867. That it is also the signed 32-bit ceiling is a coincidence of the same exponent — the two facts have nothing to do with each other.
About this page's data
Mathematical facts:computed directly from the number's value — nothing to source or verify externally.
Contextual records: 5 reviewer-confirmed records, sourced and reviewed before publication.
Last reviewed: 15 July 2026