Prime numbers
A prime has exactly two divisors: 1 and itself. There are 168 of them below 1000, and the list here is generated by a sieve rather than copied from anywhere.
Updated on October 7, 2026
All the primes up to 1000
Note that 1 is not prime — it has only one divisor, and admitting it would break the uniqueness of prime factorisation — and 2 is the only even prime.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997
- How many primes ≤ 1000
- 168
- How many primes ≤ 100
- 25
- Twin prime pairs ≤ 1000
- 35
- Largest known prime
- 2^136279841 − 1 — 41,024,320 digits
Source: Cálculo próprio a partir dos dados citados nesta página
The sieve of Eratosthenes
Write every number from 2 up to your limit. Circle 2, then cross out every multiple of 2. Move to the next uncrossed number, 3, circle it, cross out its multiples. Repeat. When the next uncrossed number exceeds the square root of your limit you can stop: everything still standing is prime. That is the whole algorithm, it is about 2,200 years old, and it is still the fastest simple way to list all primes in a range.
The square-root shortcut also tells you how to test a single number by hand. To check 997, you only need to try dividing by primes up to 31, because any factor larger than √997 would have to pair with one smaller than it. Nine trial divisions and you are done.
Source: Cálculo próprio a partir dos dados citados nesta página
How far they go, and the largest one known
There are infinitely many primes, which Euclid proved around 300 BC with an argument that still fits in a paragraph: multiply any finite list of primes together, add 1, and the result is divisible by none of them, so some prime was missing from the list. They thin out as you climb — the chance that a number near n is prime is about 1/ln n — but they never stop.
The largest prime known is 2^136279841 − 1, found by the GIMPS distributed project in October 2024. It has 41,024,320 digits: printed at normal size it would run to tens of thousands of pages. Record primes are almost always Mersenne primes, of the form 2^p − 1, because there is a fast specialised test for that shape.
How to read this page
How to read the numbers here
Every value on "Prime numbers" comes from the source named beside its section, never from an estimate of our own with no origin.
Where the data comes from
Each section of "Prime numbers" names its official source; the verification date sits at the top of the page.
Linked to the rest of the module
"Prime numbers" is one of this module’s reference pages; the glossary below defines the technical terms used here.
More about “Prime numbers”
How the density of primes drops
25.0% of the numbers up to 100 are prime, but that share falls to 16.8% up to 1,000. There are 35 twin-prime pairs in that range — and the full list on "Prime numbers" is the raw material to see that thinning with your own eyes, not just as a formula.
Words on this page
Standard uncertainty
The margin attached to a measured value, usually written in parentheses on the last digits. A constant that is "exact by definition" has zero standard uncertainty; a measured one, like the gravitational constant G, always carries some.
Standard definition by BIPM — Bureau International des Poids et Mesures (SI) · Standard uncertainty
Mole
The SI counting unit for atoms, molecules or other entities: one mole is exactly 6.02214076 × 10²³ of them, by the definition fixed in 2019. It is what ties a mass in grams to a number of particles.
Standard definition by BIPM — Bureau International des Poids et Mesures (SI) · Mole
Atomic number
The number of protons in an atom’s nucleus, written Z. It is this number, not the mass, that defines which element an atom is: every atom with 8 protons is oxygen, whether it has 8 or 18 neutrons.
Standard definition by IUPAC · Atomic number
Atomic weight
The average weight of an element’s atoms, weighted by how abundant each isotope is in nature, in atomic mass units. For 14 elements CIAAW publishes a range instead of a single value, because that abundance varies a little from sample to sample.
Standard definition by CIAAW — Commission on Isotopic Abundances and Atomic Weights · Atomic weight