The First 1,000 Prime Numbers

The first 1,000 prime numbers range from 2 (the only even prime) up to 7,919. This table provides a standard mathematical reference for prime distributions, gaps, and specialized prime families across the first several thousand integers.

Special Types of Primes in the First 1,000

Several well-known families of prime numbers appear in the first 1,000 primes. You can read more about these classifications in our guide to different types of prime numbers.

1. Mersenne Primes

A Mersenne prime takes the form M_p = 2^p - 1, where p is prime. There are exactly 4 Mersenne primes among the first 1,000 primes:

• M₂: 2² - 1 = 3 (Rank: 2nd prime)
• M₃: 2³ - 1 = 7 (Rank: 4th prime)
• M₅: 2⁵ - 1 = 31 (Rank: 11th prime)
• M₇: 2⁷ - 1 = 127 (Rank: 31st prime)

The next Mersenne prime, M₁₃ = 2¹³ - 1 = 8,191, is the 1,028th prime number, falling just beyond this group. Mersenne primes are also central to the search for record-breaking values; read more in our article on a very large prime number.

2. Twin Primes

Twin primes are pairs of prime numbers that differ by exactly 2 (i.e. (p, p + 2)). There are 174 twin prime pairs in the first 1,000 primes:

• First 5 twin pairs: (3, 5), (5, 7), (11, 13), (17, 19), and (29, 31).
• Last twin pairs in this range: (7589, 7591), (7757, 7759), and (7877, 7879).

In total, 347 of the first 1,000 primes (almost 35%) belong to at least one twin prime pair (note that 5 belongs to two pairs: (3, 5) and (5, 7)).

3. Fermat Primes

Fermat primes are primes of the form F_n = 2²ⁿ + 1. Four of the five known Fermat primes fall within the first 1,000 primes:

• F₀: 2¹ + 1 = 3 (Rank: 2nd prime)
• F₁: 2² + 1 = 5 (Rank: 3rd prime)
• F₂: 2⁴ + 1 = 17 (Rank: 7th prime)
• F₃: 2⁸ + 1 = 257 (Rank: 55th prime)

The only other known Fermat prime is F₄ = 65,537 (the 6,543rd prime).

4. Sophie Germain Primes

A prime p is a Sophie Germain prime if 2p + 1 is also prime. Within the first 1,000 primes, exactly 167 primes satisfy this condition (16.7%), beginning with 2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, 131, 173, 179, 191, 233, 239, 251, .... Their counterparts (2p + 1) are known as safe primes and are widely used in cryptography.

5. Cousin & Sexy Primes

Pairs differing by 4 are called cousin primes, while pairs differing by 6 are called sexy primes (from the Latin sex for six):

• Cousin prime pairs (gap of 4): 170 pairs in the first 1,000 primes (e.g. (7, 11), (13, 17), (19, 23)).
• Sexy prime pairs (gap of 6): 343 pairs in the first 1,000 primes (e.g. (5, 11), (7, 13), (11, 17), (17, 23)).

6. Palindromic Primes

Primes that read identically backwards and forwards in base 10. There are 20 palindromic primes in the first 1,000 primes:

Complete Table of the First 1,000 Prime Numbers

Below is the complete, indexed list of all 1,000 prime numbers arranged in 5 columns of 200 rows:

Explore More Prime Number Topics

Learn more about primes across our guides:

• Prime Number Check: Check an integer directly in your browser.
• The First 1,000,000 Prime Numbers: Distribution and milestones up to 15,485,863.
• Different Types of Prime Numbers: Detailed breakdown of Mersenne, Fermat, and twin primes.
• A Very Large Prime Number: Discover the largest known primes in mathematics.
• Prime Money Prizes: Cash awards for discovering record-breaking primes.
• Sieve of Eratosthenes: How to efficiently generate primes algorithmically.