What is the greatest integer that is the sum of two different prime nu

Prime numbers must be less different and less than 50.
Two maximum prime numbers which are less than 50 are 47 and 43

47+43 = 90.

Solution

• Greatest value of the sum of two different prime numbers, each of which <50.

• Sum = a+b. Both a and b must be prime and must be <50.
• For sum to be greatest, both a and b should be maximum.

o Thus we need to find two distinct prime numbers which are immediately less than 50
.

• Checking for 49, \(49 = 7^2\), thus is not a prime number.
• Checking for 47, we cannot prime factorize it to any prime factor <47. Thus it is prime.
• Checking for 45, \(45 = 5*3^2\), thus is not a prime.
• Checking for 43, we cannot prime factorize it to any prime factor <43. Thus it is prime.

Solution

• Greatest value of the sum of two different prime numbers, each of which <50.

• Sum = a+b. Both a and b must be prime and must be <50.
• For sum to be greatest, both a and b should be maximum.

o Thus we need to find two distinct prime numbers which are immediately less than 50
.

• Checking for 49, \(49 = 7^2\), thus is not a prime number.
• Checking for 47, we cannot prime factorize it to any prime factor <47. Thus it is prime.
• Checking for 45, \(45 = 5*3^2\), thus is not a prime.
• Checking for 43, we cannot prime factorize it to any prime factor <43. Thus it is prime.