The first four primes have this property: 17 = 2 + 3 + 5 + 7 (all primes). So does 23 (2+3+7+11)
The prime numbers 3 an 7 are both odd and sum to 10.
Sure. All composite numbers can be written as a product of primes. It shouldn't be tough to find a composite number that's the sum of three other composite numbers. Let's try 30. 2 x 3 x 5 = 30 Product of primes, check. 6 (2 x 3) + 10 (2 x 5) + 14 (2 x 7) = 30 Sum of three products of primes, check.
Prime numbers that differ from each other by exactly 2 are twin primes. Examples of twin primes are 3 and 5, 17 and 19, 599 and 601.
14 and 17
The first four primes have this property: 17 = 2 + 3 + 5 + 7 (all primes). So does 23 (2+3+7+11)
It is: 2+3+5+7 = 17
Not true. 2 + 3 = 5, where all three are primes. One of the primes in the sum must be 2, otherwise both primes would be odd and their sum would be even (and >2) and therefore not prime. Such primes: p and p+2 [3 and 5 in the above example] are known as twin primes and there are infiitely many twin primes.
The prime numbers 3 an 7 are both odd and sum to 10.
43 + 7 = 50 17 + 19 = 36 41 + 3 = 44
34 = 17+17 34 = 23 + 11 34 = 29 + 5 34 = 31 + 3
Sure. All composite numbers can be written as a product of primes. It shouldn't be tough to find a composite number that's the sum of three other composite numbers. Let's try 30. 2 x 3 x 5 = 30 Product of primes, check. 6 (2 x 3) + 10 (2 x 5) + 14 (2 x 7) = 30 Sum of three products of primes, check.
3 prime numbers which have the sum of 132: 2 + 3 + 127 2 + 17 + 113
Prime numbers that differ from each other by exactly 2 are twin primes. Examples of twin primes are 3 and 5, 17 and 19, 599 and 601.
43
100 can be expressed as the sum of two primes in 6 different ways (ignoring order): 100 = 3+97 = 11+89 = 17+83 = 29+71 = 41+59 = 47+53
7+10=17 so the sum is 17. 10-7=3 so the difference is 3. Therefore, the two numbers are 10 and 7.