Fiddler

primes = list(map(int, open("primes.txt").read().split()))
primes

for i in range(3, 11) :
    print("\nThe sum of the first p primes are divisible by {}.  p can be:".format(i))
    p = []
    for j in range(1000) :
        if sum(primes[0:j]) % i == 0 :
            p.append(j)
    print(p[0:20])

The sum of the first p primes are divisible by 3.  p can be:
[0, 10, 16, 18, 20, 24, 26, 28, 30, 32, 34, 36, 40, 42, 44, 46, 52, 54, 57, 68]

The sum of the first p primes are divisible by 4.  p can be:
[0, 5, 9, 11, 15, 17, 19, 21, 25, 27, 29, 31, 33, 35, 37, 45, 49, 71, 79, 81]

The sum of the first p primes are divisible by 5.  p can be:
[0, 2, 3, 9, 11, 17, 25, 29, 31, 51, 53, 57, 62, 71, 77, 85, 89, 91, 101, 103]

The sum of the first p primes are divisible by 6.  p can be:
[0, 57, 97, 99, 103, 105, 107, 111, 113, 119, 121, 123, 125, 127, 129, 161, 163, 169, 175, 177]

The sum of the first p primes are divisible by 7.  p can be:
[0, 5, 8, 13, 22, 33, 40, 47, 50, 56, 63, 72, 84, 86, 104, 106, 110, 115, 126, 128]

The sum of the first p primes are divisible by 8.  p can be:
[0, 11, 15, 17, 19, 21, 27, 29, 31, 37, 49, 71, 79, 83, 85, 95, 99, 101, 103, 107]

The sum of the first p primes are divisible by 9.  p can be:
[0, 20, 24, 26, 30, 40, 42, 52, 74, 78, 80, 88, 113, 119, 127, 163, 177, 179, 187]

The sum of the first p primes are divisible by 10.  p can be:
[0, 3, 9, 11, 17, 25, 29, 31, 51, 53, 57, 71, 77, 85, 89, 91, 101, 103, 105, 131]

Setup

Rohan Lewis

2026.03.29