We are six little prime brothers. All our ages add up to the age of our abundant and old dad who is obviously not in his prime.

However, if you pair him up with either of the prime neighbors, they can have a prime party.

Additionally, any five of our ages add up to a prime.

Deductive logic and small calculations might be enough to find us. Who are we?

Based on some initial comments, I will add few more comments: none of the brothers were born at the same time, and their dad is abundant and has seen all the Super Bowls since their inception.

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    $\begingroup$ (I'm going to point out, again, that your posts are increasingly less puzzle solving and more exhausting a search space for things that fit a pattern. Particularly when they're unbounded by even a no-computers tag, and when you're posting them as quickly as you have been, these questions start feeling mechanical and uninteresting as puzzles. This gets even worse when, as for the past few things you've posted, there isn't even a unique solution. You may need to change your approach here to avoid genre fatigue or solver frustration leading to downvotes.) $\endgroup$ – Rubio May 6 '19 at 20:21
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    $\begingroup$ 'little' comparatively to infinity doesn't mean much :) $\endgroup$ – JMP May 6 '19 at 20:22
  • $\begingroup$ This has unique solution and it is not unbounded as I have given enough clues to limit the size of the number...I will be mindful of comments in future posts $\endgroup$ – Uvc May 6 '19 at 20:31

The sons are

5, 7, 11, 19, 29, and 37. (All primes.)

The dad is

5+7+11+19+29+37 = 108 (an abundant non-prime number).
Any five of the sons' ages sum to a prime (71, 79, 89, 97, 101, and 103).
His neighbors are both primes (107 and 109).
The "parties" (concatenations of the father's age with a neighbor)
    are 108107 and 108109 — also primes.
Our virile father then sired his youngest at the venerable age of 103. Impressive!

To address the added comments, the sons' ages are all unique, the father's age is an abundant number, and the father is old enough to have seen the first Super Bowl in 1967.

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  • $\begingroup$ Perhaps (comparatively) prime refers to a relative relationship. $\endgroup$ – noedne May 6 '19 at 20:31
  • $\begingroup$ Read the first sentence..sons ages add upto his abundant dads age $\endgroup$ – Uvc May 6 '19 at 20:54
  • $\begingroup$ @Uvc ... they do? the 6 ages given add up to the dad's given age. $\endgroup$ – Rubio May 6 '19 at 20:55
  • $\begingroup$ @Uvc If "party" means the dad's age plus a neighbor's age must also be prime, for both neighbors, then there are no solutions I can find for a father's age under 200. Can you clarify what you mean by "prime party" here? $\endgroup$ – Rubio May 6 '19 at 21:07
  • $\begingroup$ Just a party of two concatenations..meant nothing more than that $\endgroup$ – Uvc May 6 '19 at 21:11

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