8,128
8128 is the fourth perfect number: it equals the sum of its proper divisors.
- Even
- Composite
Where 8,128 fits
Why 8,128 is special
8128 was the last perfect number known to the ancient world, and it sat there for a very long time — the fifth, 33,550,336, was not recorded until the fifteenth century. It follows 6, 28 and 496, fits Euclid's construction as 2⁶ × (2⁷ − 1) with 127 prime, and like every known perfect number it is even.
8,128 connects to:
- 496 — appears alongside
Same number, different meanings
How 8,128 is understood across different contexts — never implying one meaning because of another.
- Mathematics
8128 was the last perfect number known to the ancient world, and it sat there for a very long time — the fifth, 33,550,336, was not recorded until the fifteenth century. It follows 6, 28 and 496, fits Euclid's construction as 2⁶ × (2⁷ − 1) with 127 prime, and like every known perfect number it is even.
- History
6, 28, 496 and 8128 were all known in antiquity and appear in Nicomachus. The fifth perfect number, 33,550,336, was not recorded until the fifteenth century — a gap of well over a thousand years, because finding it meant testing whether a much larger Mersenne candidate is prime, which is hard without notation and mechanical calculation.
- Religion & belief
Augustine wrote in The City of God that six is a perfect number and that God created the world in six days because the number is perfect, rather than the number being perfect because of the creation. Medieval commentators extended the reasoning to the sequence, and the four numbers known then — 6, 28, 496 and 8128 — were sometimes matched to a scheme of the ages of the world. This is a documented history of interpretation, not a claim about the numbers.
8,128 is part of
Factors & digit properties
- Divisors (14)
- 1, 2, 4, 8, 16, 32, 64, 127, 254, 508, 1016, 2032, 4064, 8128
- Prime factorisation
- 2^6 × 127
- Digit sum
- 19
- Digital root
- 1
Representations
- Decimal
- 8128
- Scientific notation
- 8.128 × 10^3
Roman numerals
Roman numerals as modelled here goes up to 3,999.
Binary
1 1 1 1 1 1 1 0 0 0 0 0 0
1 × 4,096 + 1 × 2,048 + 1 × 1,024 + 1 × 512 + 1 × 256 + 1 × 128 + 1 × 64 + 0 × 32 + 0 × 16 + 0 × 8 + 0 × 4 + 0 × 2 + 0 × 1 = 8,128
Octal
1 7 7 0 0
1 × 4,096 + 7 × 512 + 7 × 64 + 0 × 8 + 0 × 1 = 8,128
Hexadecimal
1 f c 0
1 × 4,096 + f × 256 + c × 16 + 0 × 1 = 8,128
Read as powers of two: 4,096 + 2,048 + 1,024 + 512 + 256 + 128 + 64 = 8,128.
In historical numeral systems
Egyptian
8 lotuses, 1 coil of rope, 2 hobbles, 8 strokes
8 × 1,000 + 1 × 100 + 2 × 10 + 8 × 1 = 8,128. 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
- Triangular number
- Perfect number
- Happy number
- Hexagonal number
Related numbers & connections
The third and fourth perfect numbers, and the last two the ancient world knew. Both follow Euclid's construction from a Mersenne prime, and the gap after 8128 lasted well over a thousand years before the fifth was recorded.
View 496 →Numbers Around Us
- appears alongside496
why?
Strength 0.50, confidence "high".
History
6, 28, 496 and 8128 were all known in antiquity and appear in Nicomachus. The fifth perfect number, 33,550,336, was not recorded until the fifteenth century — a gap of well over a thousand years, because finding it meant testing whether a much larger Mersenne candidate is prime, which is hard without notation and mechanical calculation.
DocumentedHistoryPeriod: antiquity – 15th century
Religion & belief
Augustine wrote in The City of God that six is a perfect number and that God created the world in six days because the number is perfect, rather than the number being perfect because of the creation. Medieval commentators extended the reasoning to the sequence, and the four numbers known then — 6, 28, 496 and 8128 — were sometimes matched to a scheme of the ages of the world. This is a documented history of interpretation, not a claim about the numbers.
DocumentedReligion & beliefCulture: Western Christian traditionPeriod: 5th century CE onwards
Mathematics
8128 fits Euclid's construction as 2⁶ × (2⁷ − 1), and the second factor is 127, itself a Mersenne prime. Its proper divisors — 1, 2, 4, 8, 16, 32, 64, 127, 254, 508, 1016, 2032, 4064 — sum to exactly 8128. It is also the 127th triangular number, which is not a separate coincidence: every even perfect number is triangular, because the Euclid form is precisely the triangular-number formula applied to a Mersenne prime.
DocumentedMathematics
Common questions
Is 8,128 a prime number?
No, 8,128 is not prime.
What are the factors of 8,128?
The factors of 8,128 are 1, 2, 4, 8, 16, 32, 64, 127, 254, 508, 1016, 2032, 4064, 8128.
About this page's data
Mathematical facts:computed directly from the number's value — nothing to source or verify externally.
Contextual records: 3 reviewer-confirmed records, sourced and reviewed before publication.
Last reviewed: 15 July 2026