7

7
Basic Information
Cardinal Number	seven
Ordinal Number	seventh
Roman Numeral	VII
Greek Numeral	Ζ´
Factorization	7
Different Representations
Binary Form	1112
Ternary Form	213
Quaternary Form	134
Quinary Form	125
Senary Form	116
Septenary Form	107
Octal Form	78
Nonary Form	79
Undecimal Form	711
Duodecimal Form	712
Tridecimal Form	713
Quattuordecimal Form	714
Quindecimal Form	715
Hexadecimal Form	716
Septendecimal Form	717
Octodecimal Form	718
Novemdecimal Form	719
Vigesimal Form	720
Unvigesimal Form	721
Duovigesimal Form	722
Trevigesimal Form	723
Quattuorvigesimal Form	724
Quinvigesimal Form	725
Hexavigesimal Form	726
Septenvigesimal Form	727
Octovigesimal Form	728
Novemvigesimal Form	729
Trigesimal Form	730
Untrigesimal Form	731
Duotrigesimal Form	732
Tretrigesimal Form	733
Quattuortrigesimal Form	734
Quintrigesimal Form	735
Hexatrigesimal Form	736
Previous	5
Current	7
Next	11

7 is the fourth and last single-digit prime number. The only factors of 7 are 1 and 7. It's said to be a lucky number in some mythologies and it is a winning number in some games of chance, such as 777 being displayed on a lottery machine.

7 is the second Mersenne prime (since 2³-1=7) and a double Mersenne prime (since 3 is also a Mersenne prime), as well as the first Carol prime. The primorial of 7 is 210.

Proofs

• — 7 is divisible by 1.

• — 7 is not divisible by 2-6.

• — 7 is divisible by 7.

• Therefore, 7 has 2 factors and is a prime number.

As an Exponent of Mersenne Number

2⁷ - 1, which is the number 127, is a prime number. It is the 4th Mersenne prime.

Since 7 is a Mersenne prime, 127, being 2^23-1-1, is a double Mersenne prime.

Relationship with other odd numbers

The numbers before

• The previous odd number, 5, is a prime number.
  • There are no odd numbers between 5 and 7. As a result, they are twin primes.
• The odd number previous to 5 is 3. 3 is a prime number.
  • The difference between 7 and 3 is 4. Therefore, they are cousin primes.

The numbers after

• The next odd number, 9, is a square number (3²) and the first odd composite number.
• 11, the odd number following 9, is a prime number.
  • The difference between 11 and 7 is 4. Therefore, they are cousin primes, and 7 is part of a cousin prime triplet.
• 13, the odd number following 11, is a prime number.
  • The difference between 13 and 7 is 6. Therefore, they are sexy primes.

Trivia

• 7 is the last prime number whose term in the sequence is less than twice. For example, 7, which is 4th prime number, satisfies the condition. 4*2=8, so 7 is less than 8. There are only 3 such numbers in total, 3, the 2nd prime number 2*2=4, so 3 is less than 4, and 5 is the 3rd prime number, 3*2= 6, so 5 is less than 6. From 11 it will not be possible because 11 is the 5th term, and (5*2=10), so less than 11, the same 13 (6*2=12) or 17 (7*2=14), here we have as many as 3 more.
• There is a first prime number, with gap of 4 between the next prime number (11).
• 7 is the only number that is part of both cousin prime pairs, (3, 7) and (7, 11).
• There are only three consecutive odd prime numbers: 3, 5, 7, and 7 is one of them. That becomes impossible immediately after this triplet because every 3rd positive integer is divisible by 3.
• In Final Fantasy VII, there's an easter egg called All Lucky 7s, where if the character has 7777 HP, they will enter the state, launching a barrage of 64 hits, each of them doing 7777 damage.
• In the Bee Swarm Simulator from Roblox, there is a type of cog with the number on it, called 7-Pronged Cogs since November 23, 2020.

Prime Numbers 1-1,000