Prime Numbers

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

Enter the largest value:
Primes between 2 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

Prime Factors

A tool to generate the prime factors of a given positive integer

Enter a value:

Goldbach's Conjecture

Goldbach's conjecture states that every even integer greater than two is the sum of two prime numbers.

This tool finds all the different sums of two prime numbers for every even number between a given range of values.

Enter the start value:

Enter the end 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