We can next eliminate 65 because 65 is a multiple of 5. Immediately we can eliminate the EVEN NUMBERS because they are divisible by 2 and thus are not prime. Therefore, a prime number is divisible by two numbers only. The sum of prime numbers that are greater than 60 but less than 70 isĪ prime number is a number that has only two factors: 1 and itself.

Therefore the only 2 primes in the set are 61 and 67.ĭoes anyone know a good way to check for divisibility by 7? Thanks. This does not work when applied to 61 or 67 and is redundant for 63 (we knocked 63 out in the 'For 3' rule). Since neither 61 nor 67 is even, 8 cannot be a divisor.įor 9: Add up all the digits and see if the resulting sum is divisible by 9. You know 2 is a prime factor of 8 meaning any number that has 8 as a multiple must be even. I didn't stick to this rule when using the divisibility rules approach. Does anyone know a quick way to check for divisibility by7? Regardless, you can run through the multiples of 7 and realize none fall on 61 or 67 so this divisor doesn't check out.įor 8: If the last 3 digits are divisible by 8, then the whole number is divisible by 8. I recommend long-division or mental math. This does not apply to 61 and 67 since neither is divisible by 2 or 3.įor 7: No concise rule that I know of. This eliminates 65, leaving only 61 and 67 in the running for primes.įor 6: If the number is divisible by BOTH 2 & 3 (see first two rules), then the number is also divisible by 6. This does not apply to any of our remaining numbers - 61, 65, and 67.įor 5: All numbers ending in 5 or 0. This eliminates both 63 and 69.įor 4: If the last 2 digits of the number are divisible by 4, the entire number is divisible by 4. If the sum is divisible by 3, the number is divisible by 3. This eliminates 62, 64, 66, and 68.įor 3: Add up all the digits of the number.

The second way - applying divisibility rules - seems more elegant and more efficient in the long run:įor 2: All even numbers. That leaves you with 2 primes - 61 and 67 - the sum of which is 128. 63 and 69 are divisible by 9 and 3 respectively (just plug and chug). You know the even numbers - 62, 64, 66, and 68 will never be prime. The first way used a combination of pure processing power and logic.

A big list of prime numbers up to 100