641
641 is the prime factor Euler found in 1732 that disproved Fermat's conjecture about his own numbers.
- Odd
- Prime
Where 641 fits
Why 641 is special
Fermat believed every number of the form 2^(2ⁿ) + 1 was prime, and the first five are. The sixth, 4,294,967,297, is not: it is 641 × 6,700,417. Euler found the factor by reasoning about what form a factor would have to take rather than by searching, which is why the result arrived ninety years after the conjecture.
641 is part of
Factors & digit properties
- Divisors (2)
- 1, 641
- Prime factorisation
- 641
- Digit sum
- 11
- Digital root
- 2
Representations
- Decimal
- 641
- Scientific notation
- 6.410 × 10^2
Roman numerals
D C X L I
DCXLI uses the subtractive pair XL: ten before fifty — fifty minus ten.
Binary
1 0 1 0 0 0 0 0 0 1
1 × 512 + 0 × 256 + 1 × 128 + 0 × 64 + 0 × 32 + 0 × 16 + 0 × 8 + 0 × 4 + 0 × 2 + 1 × 1 = 641
Octal
1 2 0 1
1 × 512 + 2 × 64 + 0 × 8 + 1 × 1 = 641
Hexadecimal
2 8 1
2 × 256 + 8 × 16 + 1 × 1 = 641
Read as powers of two: 512 + 128 + 1 = 641.
In historical numeral systems
Egyptian
6 coils of rope, 4 hobbles, 1 stroke
6 × 100 + 4 × 10 + 1 × 1 = 641. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.
Babylonian
1 corner wedge (sixties place), 4 corner wedges + 1 vertical wedge (units place)
10 × 60 + 41 = 641. Places are separated by a space on the tablet, with the higher place written first.
Greek (Ionic)
chi, then mu, then alpha, marked as a numeral
chi-mu-alpha + keraia
chi + mu + alpha written in descending order and added — the letters carry their values wherever they stand, so this is addition, not place value.
Hebrew numerals
tav, then resh, then mem, then alef
tav-resh-mem-alef
tav (400) + resh (200) + mem (40) + alef (1) = 641, written in descending order.
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
- Sophie Germain prime
- Twin prime
Related numbers & connections
641 appears in Numbers in measurement, the topic covering numbers that carry a documented measurement fact.
Numbers Around Us
- appears inUnits and measurement
why?
Strength 0.50, confidence "high".
Science
The factor that disproved Fermat's conjecture about his own numbers is 641 (worldwide, number theory). Euler found in 1732 that the sixth Fermat number is 641 × 6,700,417. He reasoned about what form a factor must take rather than searching, which is why the result took ninety years.
DocumentedScienceGeography: worldwide, number theory
Common questions
Is 641 a prime number?
Yes, 641 is prime — it has exactly two positive divisors: 1 and itself.
What are the factors of 641?
The factors of 641 are 1, 641.
What is 641 in Roman numerals?
641 in Roman numerals is DCXLI. XL is subtractive: ten before fifty — fifty minus ten. Written additively it would be DCXXXXI, which Roman inscriptions used freely — the strict subtractive form is a later convention.
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