EXPRESSING A NUMBER AS THE SUM OF PRIME NUMBERS

Example 1 :

Express 5 as the sum of two consecutive primes.

Solution :

5 = 2 + 3

Example 2 :

Express 7 as the sum of any two different primes.

Solution :

7 = 2 + 5

Example 3 :

Express 8 as the sum of two consecutive primes.

Solution :

8 = 3 + 5

Example 4 :

Express 10 as the sum of any two different odd primes.

Solution :

10 = 3 + 7

Example 5 :

Express 10 as the sum of three consecutive primes.

Solution :

10 = 2 + 3 + 5

Example 6 :

Express 12 as the sum of two consecutive primes.

Solution :

12 = 5 + 7

Example 7 :

Express 17 as the sum of any four diffferent primes.

Solution :

17 = 2 + 3 + 5 + 7

Example 8 :

Express 18 as the sum of any three different primes.

Solution :

18 = 2 + 3 + 13

Example 9 :

Express 20 as the sum of any two diffferent primes.

Solution :

20 = 7 + 13

Example 10 :

Express 20 as the sum of any two diffferent primes.

Solution :

20 = 7 + 13

Example 11 :

Express 20 as the sum of any three diffferent primes.

Solution :

20 = 2 + 7 + 11

Example 12 :

Express 21 as the sum of any four diffferent primes.

Solution :

21 = 2 + 3 + 5 + 11

Example 13 :

Express 22 as the sum of any three diffferent primes.

Solution :

22 = 2 + 3 + 17

Example 14 :

Express 23 as the sum of any four diffferent primes.

Solution :

23 = 2 + 3 + 5 + 13

Example 15 :

Express 24 as the sum of any three diffferent primes.

Solution :

24 = 2 + 3 + 19

Example 16 :

Express 25 as the sum of any two diffferent primes.

Solution :

25 = 2 + 23

Example 17 :

Express 26 as the sum of any two diffferent primes.

Solution :

26 = 3 + 23

Example 18 :

Express 26 as the sum of any four diffferent primes.

Solution :

26 = 3 + 5 + 7 + 11

Example 19 :

Express 27 as the sum of any four diffferent primes.

Solution :

27 = 2 + 3 + 5 + 17

Example 20 :

Express 27 as the sum of any three diffferent primes.

Solution :

27 = 3 + 5 + 19

Example 21 :

Express 28 as the sum of any three diffferent primes.

Solution :

28 = 2 + 3 + 23

Example 22 :

Express 29 as the sum of any four diffferent primes.

Solution :

29 = 2 + 3 + 5 + 19

In the table shown below, the crossed-out numbers are composite and the coloured numbers (encircled) are primes.

Using the table above, answers the questions in the following examples.

Example 23 :

Express 42 as the sum of two consecutive primes.

Solution :

42 = 19 + 23

Example 24 :

Express 68 as the sum of two consecutive primes.

Solution :

68 = 31 + 37

Example 25 :

Express 100 as the sum of two consecutive primes.

Solution :

100 = 47 + 53

Example 26 :

Express 128 as the sum of two consecutive primes.

Solution :

128 = 61 + 67

Example 27 :

Express 31 as the sum of any three odd primes.

Solution :

31 = 5 + 7 + 19

Example 28 :

Express 55 as the sum of any three odd primes.

Solution :

55 = 3 + 23 + 29

Example 29 :

Express 79 as the sum of any three odd primes.

Solution :

79 = 19 + 29 + 31

Example 30 :

Express 104 as the sum of any three primes.

Solution :

104 = 2 + 19 + 83

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