every number greater than 2 can be written as the sum of two prime numbers.
22=3+19 or 22=11+11
write the even number from 80 to 96 adbthe sum of two primes in atleast one way.
This is the Goldbach Conjecture. The conjecture has been shown to hold up through 4 × 10^18, but has not yet been proven for all integers.
Anyway, just start listing them. A good place to start is near the midpoint of possibilities. Note that an odd number must be the sum of an even number and an odd number. The only even prime is 2.
80 = 39+41? no
80 = 37+43? yes
81 = 2 + 79
82 = 29+53
...
To find even numbers from 80 to 96 that can be written as the sum of two prime numbers, we can check each number individually:
80: 80 is even, but it cannot be written as the sum of two prime numbers.
81: 81 is odd, so we skip it.
82: 82 = 41 + 41. Both 41 and 41 are prime numbers, so 82 can be written as the sum of two primes.
83: 83 is a prime number, so it cannot be expressed as the sum of two primes.
84: 84 = 43 + 41. Both 43 and 41 are prime numbers, so 84 can be written as the sum of two primes.
85: 85 is odd, so we skip it.
86: 86 = 43 + 43. Both 43 and 43 are prime numbers, so 86 can be written as the sum of two primes.
87: 87 is odd, so we skip it.
88: 88 = 43 + 45. We can't find two prime numbers that sum up to 45.
89: 89 is a prime number, so it cannot be expressed as the sum of two primes.
90: 90 = 47 + 43. Both 47 and 43 are prime numbers, so 90 can be written as the sum of two primes.
91: 91 is odd, so we skip it.
92: 92 = 41 + 51. We can't find two prime numbers that sum up to 51.
93: 93 is odd, so we skip it.
94: 94 = 47 + 47. Both 47 and 47 are prime numbers, so 94 can be written as the sum of two primes.
95: 95 = 47 + 48. We can't find two prime numbers that sum up to 48.
96: 96 = 47 + 49. Both 47 and 49 are prime numbers, so 96 can be written as the sum of two primes.
Therefore, the even numbers from 80 to 96 that can be written as the sum of two prime numbers are: 82, 84, 86, 90, 94, and 96.
To find the even numbers from 80 to 96 that can be written as the sum of two prime numbers, we need to check each even number in that range.
Let's start with 80. To determine if it can be written as the sum of two prime numbers, we'll check all pairs of prime numbers that add up to 80.
Checking the prime numbers:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79.
Taking pairs from the above list, we can check the sums:
2 + 78 = 80 (Not prime)
3 + 77 = 80 (Not prime)
5 + 75 = 80 (Not prime)
7 + 73 = 80 (Not prime)
11 + 69 = 80 (Not prime)
13 + 67 = 80 (Not prime)
17 + 63 = 80 (Not prime)
19 + 61 = 80 (Prime!)
So, 80 can be written as the sum of two prime numbers: 80 = 19 + 61.
Repeating the same process for each even number from 80 to 96, we get:
82 = 43 + 39 (Not prime)
84 = 43 + 41 (Prime!)
86 = 43 + 43 (Not prime)
88 = 43 + 45 (Not prime)
90 = 43 + 47 (Prime!)
92 = 43 + 49 (Not prime)
94 = 43 + 51 (Not prime)
96 = 43 + 53 (Prime!)
Therefore, the even numbers from 80 to 96 that can be written as the sum of two prime numbers are:
80 = 19 + 61
84 = 43 + 41
90 = 43 + 47
96 = 43 + 53