Cousin Prime Numbers Definition with Examples (original) (raw)
Last Updated : 23 Jul, 2025
Cousin primes are pairs of prime numbers that differ by exactly 4. In other words, for two prime numbers p and q, if q = p + 4, and both p and q are primes, then (p, q) is a pair of cousin primes. For example, the prime numbers 3 and 7 are cousin primes because 7 - 3 = 4.
Some other examples of Cousin Primes are:
| **Cousin Prime Pair | **Difference |
|---|---|
| (3, 7) | 7 - 3 = 4 |
| (7, 11) | 11 - 7 = 4 |
| (13, 17) | 17 - 13 = 4 |
| (19, 23) | 23 - 19 = 4 |
| (31, 35) | 35 - 31 = 4 |
| (37, 41) | 41 - 37 = 4 |
| (43, 47) | 47 - 43 = 4 |
| (67, 71) | 71 - 67 = 4 |
| (79, 83) | 83 - 79 = 4 |
| (97, 101) | 101 - 97 = 4 |
**Fact about Cousin Primes
Some interesting facts about cousin primes are:
- The only prime belonging to two pairs of cousin primes is 7.
- It is believed that there are infinitely many cousin primes, although this has not been proven yet.
- As of April 2022, the largest known cousin primes are:
p = 29055814795 × (2172486 − 286243) + 286245 - 3
p + 4 = 29055814795 × (2172486 − 286243) + 286245 + 1.
These were found by S. Batalov and have 51,934 digits each.
Cousin, Twin and Sexy Primes
Cousin, twin, and sexy primes are considered similar types of primes, where two primes differ by a specific finite number.
| **Prime Type | **Definition | **Examples |
|---|---|---|
| **Cousin Primes | A pair of prime numbers that differ by 4. | (3, 7), (7, 11), (13, 17), (19, 23) |
| **Twin Primes | A pair of prime numbers that differ by 2. | (3, 5), (11, 13), (17, 19), (29, 31) |
| **Sexy Primes | A pair of prime numbers that differ by 6. | (5, 11), (7, 13), (11, 17), (13, 19) |
**Conclusion
We can say that **cousin primes are pairs of prime numbers that have a difference of 4. They are part of a fascinating group of prime numbers, like twin primes and sexy primes, that highlight unique patterns in the number system.
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