List of primes

Primes generated using the prime sieve of Eratosthenes

Enter the largest value:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97,

List of primes

The prime sieve of Eratosthenes

Generating primes to a maximum value of n
  • Create a grid with the number values from 1 to n
  • Highlight all of the grid values except for the value 1
  • Calculate x, the square root of n rounded down.
  • Move through the grid starting at 2 and up to the value of x
  • If a highlighted value if found, unhighlight all of the multiples of that value in the grid
  • When the process has been completed, the remaining hightlighted values are the prime numbers
Example: primes between 1 and 100
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100

Square root of 100 is 10

Starting value is 2

Factors: 0

Enter a value:

Goldbach's Conjecture

Every even integer greater than two is the sum of two primes

Enter the first value:

Enter the largest value:

4

2 + 2

6

3 + 3

8

3 + 5

10

3 + 7, 5 + 5

12

5 + 7

14

3 + 11, 7 + 7

16

3 + 13, 5 + 11

18

5 + 13, 7 + 11

20

3 + 17, 7 + 13

22

3 + 19, 5 + 17, 11 + 11

24

5 + 19, 7 + 17, 11 + 13

26

3 + 23, 7 + 19, 13 + 13

28

5 + 23, 11 + 17

30

7 + 23, 11 + 19, 13 + 17

32

3 + 29, 13 + 19

34

3 + 31, 5 + 29, 11 + 23, 17 + 17

36

5 + 31, 7 + 29, 13 + 23, 17 + 19

38

7 + 31, 19 + 19

40

3 + 37, 11 + 29, 17 + 23

42

5 + 37, 11 + 31, 13 + 29, 19 + 23

44

3 + 41, 7 + 37, 13 + 31

46

3 + 43, 5 + 41, 17 + 29, 23 + 23

48

5 + 43, 7 + 41, 11 + 37, 17 + 31, 19 + 29

50

3 + 47, 7 + 43, 13 + 37, 19 + 31

52

5 + 47, 11 + 41, 23 + 29

54

7 + 47, 11 + 43, 13 + 41, 17 + 37, 23 + 31

56

3 + 53, 13 + 43, 19 + 37

58

5 + 53, 11 + 47, 17 + 41, 29 + 29

60

7 + 53, 13 + 47, 17 + 43, 19 + 41, 23 + 37, 29 + 31

62

3 + 59, 19 + 43, 31 + 31

64

3 + 61, 5 + 59, 11 + 53, 17 + 47, 23 + 41

66

5 + 61, 7 + 59, 13 + 53, 19 + 47, 23 + 43, 29 + 37

68

7 + 61, 31 + 37

70

3 + 67, 11 + 59, 17 + 53, 23 + 47, 29 + 41

72

5 + 67, 11 + 61, 13 + 59, 19 + 53, 29 + 43, 31 + 41

74

3 + 71, 7 + 67, 13 + 61, 31 + 43, 37 + 37

76

3 + 73, 5 + 71, 17 + 59, 23 + 53, 29 + 47

78

5 + 73, 7 + 71, 11 + 67, 17 + 61, 19 + 59, 31 + 47, 37 + 41

80

7 + 73, 13 + 67, 19 + 61, 37 + 43

82

3 + 79, 11 + 71, 23 + 59, 29 + 53, 41 + 41

84

5 + 79, 11 + 73, 13 + 71, 17 + 67, 23 + 61, 31 + 53, 37 + 47, 41 + 43

86

3 + 83, 7 + 79, 13 + 73, 19 + 67, 43 + 43

88

5 + 83, 17 + 71, 29 + 59, 41 + 47

90

7 + 83, 11 + 79, 17 + 73, 19 + 71, 23 + 67, 29 + 61, 31 + 59, 37 + 53, 43 + 47

92

3 + 89, 13 + 79, 19 + 73, 31 + 61

94

5 + 89, 11 + 83, 23 + 71, 41 + 53, 47 + 47

96

7 + 89, 13 + 83, 17 + 79, 23 + 73, 29 + 67, 37 + 59, 43 + 53

98

19 + 79, 31 + 67, 37 + 61

100

3 + 97, 11 + 89, 17 + 83, 29 + 71, 41 + 59, 47 + 53

Special Primes

Mersenne Primes

Primes of the form 2n - 1

1: 21 - 1

3: 22 - 1

7: 23 - 1

31: 25 - 1

127: 27 - 1

8191: 213 - 1

131071: 217 - 1

524287: 219 - 1

2147483647: 231 - 1

Fermat Numbers

Primes of the form 2n + 1 (n is always a power of 2)

3: 21 + 1

5: 22 + 1

17: 24 + 1

257: 28 + 1

65537: 216 + 1