Problem 060

[jnash67]

Tommy137 was pointing out exactly that - the inequalities that DiogoRegateiro was using while searching for a set of 5 primes were invalid. By using the counterexample of 5 consecutive primes (consecutive so that they are approximately the same size) he showed that four of them would certainly be larger than N/2. Hence the fourth of Diogo's inequalities does not hold in general. Also, it seems to me that N was merely some arbitrary upper bound or search limit for the answer that Diogo was using.

OK. Thx.

[StephanKoehler]

I just want to point out that the given solution of four primes [3, 7, 109, 673] is actually wrong. The following sequence meets the criteria and has a lower sum [7, 9, 19, 433].
Nonetheless, using the same algorithm I was able to get the correct answer for five primes.

[mdean]

I just want to point out that the given solution of four primes [3, 7, 109, 673] is actually wrong. The following sequence meets the criteria and has a lower sum [7, 9, 19, 433].
Nonetheless, using the same algorithm I was able to get the correct answer for five primes.

9 is not prime

[PeterBurbery]

I think the set {3,7,37,73} has a lower sum.
Every number made by concatenating these is prime:
37,73,337,373,and 733.
The sum of these numbers is lower than the example:120.

[maujjy]

You are missing 737 which is 11*67.

[jaap]

As well as 377=13×29, 3773=7×7×7×11, and 7337=11×23×29.