5 Is the third prime number and the third single-digit prime. 5's prime factors are 1 and 5.
It's also the second Fermat prime. Due to the fact that the difference between the previous and next primes is 2, it's the first balanced prime and the only balanced prime to be a prime number in between that's a prime number a prime number's difference from 2 others. The primorial of 5 is 30.
Proofs
— 5 is divisible by 1.
— 5 is not divisible by 2-4.
— 5 is divisible by 5.
- Therefore it has 2 factors.
As an Exponent of Mersenne Number
25 - 1, which is the number 31, is a prime number. It is the 3rd Mersenne Prime.
Relationship with other numbers
The numbers before
- The previous natural number 4 is a first composite number, and square of 2.
- The previous odd number 3, is a prime number.
- There are no odd numbers between 3 and 5. As a result, they are twin primes.
- 2 is the lowest and only even prime number.
- 1, the number before 2, is not a prime number (a prime number has exactly 2 positive divisors; since the only positive divisor of 1 is 1, it is not prime) and the same goes for the number 0.
The numbers after
- The next number 6, is a second prime number, and first non-square composite numbers, with first two prime numbers 2*3
- The next odd number, 7, is a prime number.
- There are no odd numbers between 5 and 7. As a result, they are twin primes.
- 8, the number following 7, is a first cube number 2³.
- 9, the number following 8, is a square number. It is the first odd composite number.
- 10, the number following 9, is a composite number, and prime factors is 2*5.
- 11, the number following 10, is a prime number.
- The difference between 11 and 5 is 6, therefore they are sexy primes.
Trivia
- There are only 3 consecutive odd numbers that are primes: 3, 5, 7, and five is one of them, so 5 is the only number that is part of two twin prime pairs, (3, 5) and (5, 7), Immediately after, this becomes impossible, since every 3rd positive integer is divisible by 3 where these numbers are marked in bold (e.g. 9, 11, 13, 15, 17, 19, 21, etc. is divisible by 3).
- 5 is the first number starting the prime quadruplet [5, 7, 11, 13]. Additionally, it is the only number whose first term of the first four does not end with ...1, for example the next prime quadruplets are [11,13,17,19], [101,103,107,109], [191,193,197,199], [821,823,827,829], so the first numbers of prime quadruplets ends to 1, (11,101,191,821 etc.).
- It forms the only sexy prime quintuplet with 5, 11, 17, 23, and 29, since all multiples of 5 (except itself) are composite.
- As of February 7, 2021, the Prime Number Test on the main page of this wiki mistakenly stated that 5 is not prime.
- However, the prime tester no longer works.
- It is the only prime number with a 5 as its last digit. All other positive integers with a 5 as their last digit - 15, 25, 35, 45 are divisible by 5, thus they are composite.
- Is the only odd untouchable number.
- Is the one of two numbers that does not have a last digit 1, 3, 7 or 9, the other exception being the first prime number 2, moreover this numbers are untouchable prime numbers. Untouchable numbers are even (the exception is 5), and 2 is the only even prime number. So first two untouchable numbers, and all one-digit untouchable are prime, and the next untouchable numbers are 52, 88, 96 and 120 (so even and also composite numbers).
- It is the only prime number with only one Roman numeral digit: V.
- It is the largest prime number with only one syllable.
- It is the smallest prime number equal to the sum of two preceding prime numbers: 2 + 3 = 5.