Why do the first 1000 primes summed in triplets yield exactly 12,000 unique prime sums? /u/AmongstYou666 Python Education

Hey everyone,

I’ve been working on a project where I sum combinations of the first 1,000 prime numbers taken 3 at a time. Interestingly, I ended up with exactly 12,000 unique prime sums. I’m trying to understand the mathematical reason behind this specific number of matches.

Here are a few details for context:

• I generated the first 1,000 prime numbers.
• I then created all possible combinations of these primes, three at a time.
• After calculating the sums and filtering to keep only those sums that are prime, I ended up with 12,000 unique prime sums.

Does anyone have insights into why the number of unique prime sums from these combinations would be precisely 12,000? Is there a known mathematical property or formula that might explain this result?

Thanks in advance for your help!

Hey everyone,

I’ve been working on a project where I sum combinations of the first 1,000 prime numbers taken 3 at a time. Interestingly, I ended up with exactly 12,000 unique prime sums. I’m trying to understand the mathematical reason behind this specific number of matches.

Here are a few details for context:

• I generated the first 1,000 prime numbers.
• I then created all possible combinations of these primes, three at a time.
• After calculating the sums and filtering to keep only those sums that are prime, I ended up with 12,000 unique prime sums.

Does anyone have insights into why the number of unique prime sums from these combinations would be precisely 12,000? Is there a known mathematical property or formula that might explain this result?

Thanks in advance for your help!