Prime numbers -- only devides by 1 or itself

 There are 25 prime numbers between 1 and 100  -- Multiplying Two Primes: Is always a non-prime...

2, 3, 5, 7 (under 10)

11, 13, 17, 19 (under 20)

23, 29 (under 30)

31, 37 (under 40)

41, 43, 47 (under 50)

53, 59 (under 60)

61, 67 (under 70)

71, 73, 79 (under 80)

83, 89 (under 90)

97 (under 100) 

There are exactly 8 pairs of twin primes under 100. Twin primes are pairs of prime numbers that have a difference of exactly two. [1, 2, 3]

The 8 Twin Prime Pairs Under 100

• (3, 5)
• (5, 7)
• (11, 13)
• (17, 19)
• (29, 31)
• (41, 43)
• (59, 61)
• (71, 73)

Fast Facts About Twin Primes

• The Number 5 is unique because it belongs to two different twin prime pairs: (3, 5) and (5, 7).
• The 6n ± 1 Rule: Except for the very first pair (3, 5), the number right in the middle of every twin prime pair is always a multiple of 6 (like 12, 18, 30, 42, 60, and 72)

The 8 Cousin Prime Pairs Under 100

• (3, 7)
• (7, 11)
• (13, 17)
• (19, 23)
• (37, 41)
• (43, 47)
• (67, 71)
• (79, 83)
• The 15 Sexy Prime Pairs Under 100
  Sexy primes are pairs of prime numbers that are exactly 6 apart (named after the Latin word for six, sex). [1, 2, 3]
  • (5, 11)
  • (7, 13)
  • (11, 17)
  • (13, 19)
  • (17, 23)
  • (23, 29)
  • (31, 37)
  • (37, 43)
  • (41, 47)
  • (47, 53)
  • (53, 59)
  • (61, 67)
  • (67, 73)
  • (73, 79)
  • (83, 89)
  The 8 Prime Triplets Under 100
  A prime triplet is a set of three prime numbers where the smallest and largest numbers differ by exactly 6. They form tight clusters of either (p, p+2, p+6) or (p, p+4, p+6). [1, 2, 3]
  • (5, 7, 11)
  • (7, 11, 13)
  • (11, 13, 17)
  • (13, 17, 19)
  • (17, 19, 23)
  • (37, 41, 43)
  • (41, 43, 47)
  • (67, 71, 73)
  Prime Quadruplets Under 100

  A prime quadruplet is the closest possible spacing for four consecutive prime numbers. They always take the form (p, p+2, p+6, p+8), which actually contains two overlapping pairs of twin primes. [1, 2]

  There are only 4 prime quadruplets under 100: [1]

  • (5, 7, 11, 13)
  • (11, 13, 17, 19)
  • (101, 103, 107, 109) — (Just outside 100, but shows the pattern perfectly) [1, 2]

  Except for the very first group, the number right in the middle of a prime quadruplet always ends in a 0 (like 15, 110, etc.).

a number made by multiplying two primes has a unique property: it cannot be broken down in any other way. For example, 15 can only be made by \(3 \times 5\). It is impossible to find three other numbers that multiply to exactly 15.