+0

# Primes

0
40
2
+1347

Goldbach's conjecture states that every even number greater than two can be expressed as the sum of two prime numbers. For example, \$2022 = 191 + 1831.\$ How many ordered pairs of prime numbers have a sum of \$100 \,?\$

Jul 11, 2023

#1
+806
0

Goldbach's conjecture states that every even number greater than two can be expressed as the sum of two prime numbers. For example, \$2022 = 191 + 1831.\$ How many ordered pairs of prime numbers have a sum of \$100 \,?\$

You could list all the prime numbers up to 50.

No need to go past 50.   I counted 6 of them.

3,  11,  17,  29,  41,  47

97,  89,  83,  71,  59,  53

Can't count 2 because 98 isn't prime.

ditto   5 ... 95

ditto   7 ... 93

ditto 13 ... 87

ditto 19 ... 81

ditto 23 ... 77

ditto 31 ... 69

ditto 37 ... 63

ditto 43 ... 57

edited to add ~  I'm not certain what an "ordered" pair is.

So if the sequence matters, then it's 12.

.

Jul 11, 2023
edited by Bosco  Jul 11, 2023
#2
0

WLOG

realize for two numbers to sum up to 100, one must be < 50 (as 50 isn't prime)

There are 6 prime numbers less than 50 that satisfy our condition

And these 6 prime numbers could be placed in the x coord or the y coord

So 6*2= 12

Jul 12, 2023