65,521
65,521 is the largest prime below 2¹⁶, and the modulus used by the Adler-32 checksum.
- Odd
- Prime
Where 65,521 fits
Why 65,521 is special
Adler-32 uses it because a prime modulus spreads checksum values more evenly than a power of two, and because staying under 2¹⁶ keeps the arithmetic inside 16-bit registers. It is a good example of a number chosen for two constraints at once rather than for any property of its own.
65,521 is part of
Factors & digit properties
- Divisors (2)
- 1, 65521
- Prime factorisation
- 65521
- Digit sum
- 19
- Digital root
- 1
Representations
- Decimal
- 65521
- Scientific notation
- 6.552 × 10^4
Roman numerals
Roman numerals as modelled here goes up to 3,999.
Binary
1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1
1 × 32,768 + 1 × 16,384 + 1 × 8,192 + 1 × 4,096 + 1 × 2,048 + 1 × 1,024 + 1 × 512 + 1 × 256 + 1 × 128 + 1 × 64 + 1 × 32 + 1 × 16 + 0 × 8 + 0 × 4 + 0 × 2 + 1 × 1 = 65,521
Octal
1 7 7 7 6 1
1 × 32,768 + 7 × 4,096 + 7 × 512 + 7 × 64 + 6 × 8 + 1 × 1 = 65,521
Hexadecimal
f f f 1
f × 4,096 + f × 256 + f × 16 + 1 × 1 = 65,521
Read as powers of two: 32,768 + 16,384 + 8,192 + 4,096 + 2,048 + 1,024 + 512 + 256 + 128 + 64 + 32 + 16 + 1 = 65,521.
In historical numeral systems
Egyptian
6 fingers, 5 lotuses, 5 coils of rope, 2 hobbles, 1 stroke
6 × 10,000 + 5 × 1,000 + 5 × 100 + 2 × 10 + 1 × 1 = 65,521. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.
Systems that simply cannot reach this value are left out. Where a script needs a font most readers do not have, the reading is given instead of the glyphs — see number systems for each system in full.
Other mathematical patterns
- Deficient number
- Happy number
- Lucky number (mathematical sieve)
- Twin prime
Technology & computing
The modulus used by the Adler-32 checksum is 65,521 (worldwide, RFC 1950). The largest prime below 2¹⁶. A prime modulus spreads checksum values more evenly than a power of two, and staying under 2¹⁶ keeps the arithmetic in 16-bit registers.
DocumentedTechnology & computingGeography: worldwide, RFC 1950
Common questions
Is 65,521 a prime number?
Yes, 65,521 is prime — it has exactly two positive divisors: 1 and itself.
What are the factors of 65,521?
The factors of 65,521 are 1, 65521.
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: 15 July 2026