65,537
65,537 is the public exponent used by most RSA encryption in the world.
- Odd
- Prime
Where 65,537 fits
Why 65,537 is special
It is chosen because it is prime, is 2^16 + 1, and has only two bits set — so encryption is fast — while being large enough to avoid the attacks that broke the earlier choice of 3. It is also the largest known Fermat prime, and probably the last.
65,537 is part of
Factors & digit properties
- Divisors (2)
- 1, 65537
- Prime factorisation
- 65537
- Digit sum
- 26
- Digital root
- 8
Representations
- Decimal
- 65537
- Binary
- 10000000000000001
- Octal
- 200001
- Hexadecimal
- 10001
- Scientific notation
- 6.554 × 10^4
Other mathematical patterns
- Deficient number
- Twin prime
Related numbers & connections
Two of the five known Fermat primes. 65,537 is the largest, and is the public exponent used by most RSA encryption in the world because its bit pattern makes the arithmetic cheap.
View 257 →Shares a distinctive class
- is associated with257
why?
Strength 0.50, confidence "high".
Technology & computing
65,537 is chosen as the RSA public exponent because it is prime, is 2^16 + 1, and has only two bits set, so encryption is fast — while being large enough to avoid the attacks that made the earlier choice of 3 unsafe. It is also the largest known Fermat prime.
DocumentedTechnology & computing
Common questions
Is 65,537 a prime number?
Yes, 65,537 is prime — it has exactly two positive divisors: 1 and itself.
What are the factors of 65,537?
The factors of 65,537 are 1, 65537.
About this page's data
Mathematical facts:computed directly from the number's value — nothing to source or verify externally.
Contextual records: 1 reviewer-confirmed record, sourced and reviewed before publication.
Last reviewed: 3 August 2026