Twin Prime Finder

(p, p+2) both prime

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About Twin Prime Finder

A twin prime finder locating pairs (p, p+2) where both are prime. Searches near any number, counts twins in range, shows cousin primes (p, p+4) and sexy primes (p, p+6). Displays Brun's constant approximation. Client-side.

Twin Prime Finder Features

  • Twin pairs
  • Range search
  • Cousin/Sexy
  • Count
  • Brun's constant
Twin primes: pairs (p, p+2) where both are prime. (3,5), (5,7), (11,13), (17,19), (29,31), (41,43)... Twin prime conjecture: infinitely many exist (unproven). Zhang Yitang (2013): bounded gaps between primes. Brun's constant: Σ(1/p+1/(p+2)) ≈ 1.902.

How to Use

Enter n:

  • Twins: Pairs near n
  • Count: Twins up to n
  • Related: Cousin, sexy primes

Twin Prime Conjecture

One of the most famous open problems: are there infinitely many twin primes? Zhang (2013) proved bounded gaps ≤ 70,000,000. Maynard/Tao reduced to 246. Gap of 2 remains unproven.

Prime Gaps

  • Twin (gap 2): (11,13), (17,19)
  • Cousin (gap 4): (3,7), (7,11)
  • Sexy (gap 6): (5,11), (7,13)
  • Prime triplets: (p, p+2, p+6)

Step-by-Step Instructions

  1. 1Enter start number.
  2. 2Find twin primes.
  3. 3Count in range.
  4. 4See cousin primes.
  5. 5View related pairs.

Twin Prime Finder — Frequently Asked Questions

Are there infinitely many twin primes?+

Unknown! The twin prime conjecture is one of the biggest open problems. Yitang Zhang (2013) proved infinitely many prime pairs with gap ≤ 70,000,000. Polymath8/Maynard reduced to 246. The gap of exactly 2 remains unproven.

What is Brun's constant?+

Sum of reciprocals of twin primes: B = (1/3+1/5) + (1/5+1/7) + (1/11+1/13) + ... ≈ 1.9021605. Unlike the sum of all prime reciprocals (diverges), Brun proved this sum converges. This means twin primes are 'rare' even if infinite.

What are the largest known twin primes?+

As of 2024: 2996863034895·2^1290000±1 (388,342 digits each). Found by PrimeGrid distributed computing. Twin primes become increasingly rare: roughly n/(ln n)² twins below n.

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