- #1

FeDeX_LaTeX

Gold Member

- 437

- 13

"Determine the least possible value of the largest term in an arithmetic progression of seven distinct primes."

I really have no clue what to do here. Is there a general tactic that you can use to do this, other than trial and error? Some experimenting gives you these of arithmetic progressions:

5, 11, 17, 23, 29

5, 17, 29, 41, 53

7, 19, 31, 43

3, 7, 11

41, 47, 53, 59

61, 67, 73, 79

7, 37, 67, 97, 127, 157

107, 137, 167, 197, 227, 257

53, 113, 173, 233, 293, 353

I haven't found one that gives me a string of 7 primes yet and I've just been looking at primes under 100.

Of course there are general rules to follow when finding the strings that I spotted (shouldn't add a number to a prime which will land you on a multiple of 5, such as adding 12 to a prime excluding 2).

EDIT: Okay, I think I know how to solve this problem. If I had 4, 6 or 8, I'll never get a streak longer than 5, but if I choose a difference of +10 (or a multiple of 10), I might find one more easily.

I really have no clue what to do here. Is there a general tactic that you can use to do this, other than trial and error? Some experimenting gives you these of arithmetic progressions:

5, 11, 17, 23, 29

5, 17, 29, 41, 53

7, 19, 31, 43

3, 7, 11

41, 47, 53, 59

61, 67, 73, 79

7, 37, 67, 97, 127, 157

107, 137, 167, 197, 227, 257

53, 113, 173, 233, 293, 353

I haven't found one that gives me a string of 7 primes yet and I've just been looking at primes under 100.

Of course there are general rules to follow when finding the strings that I spotted (shouldn't add a number to a prime which will land you on a multiple of 5, such as adding 12 to a prime excluding 2).

EDIT: Okay, I think I know how to solve this problem. If I had 4, 6 or 8, I'll never get a streak longer than 5, but if I choose a difference of +10 (or a multiple of 10), I might find one more easily.

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