what are all the possible ways that 70 can be the sum of two prime numbers??
2007-08-29 08:32:59 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
70 is an even number.
Other than 2, all prime numbers are odd.
Therefore it cannot be the sum of 2 + another prime.
Next, try each prime number in turn and check:
70 - 3 = 67 yes (3 and 67 are prime)
70 - 5 = 65 (65 is not prime: divisible by 5)
70 - 7 = 63 (63 not prime: divible by 3)
and so on.
You can stop when the number being subtracted gets bigger than the remainder.
2007-08-29 08:41:05 · answer #1 · answered by Raymond 7 · 0⤊ 0⤋
Let's make a list of prime numbers between 1 and 35:
(Because if the first number is less than 35, the second is larger)
2,3,5,7,11,13,17,19,23,29,31
70-2=68=2*34
70 - 3 = 67
70-5=65=5*13
70-7=63=7*9
70-11=59
70-13=57=3*19
70-17=53
70-19=51=3*17
70-23=47
70-29=41
70-31=39=3*13
So, the ways are:
3+67, 11+59, 17+53, 23+47, 29+41
2007-08-29 15:45:08 · answer #2 · answered by Amit Y 5 · 0⤊ 0⤋
3+67
11+59
17+53
23+47
29+41
2007-08-29 15:41:46 · answer #3 · answered by Anonymous · 1⤊ 0⤋