Stern primes: prime p where p≠q+2ab for any smaller prime q and a,b≥1. Known: 2,3,17,137,227,977,1187,1493... Conjectured finite — possibly only finitely many exist. Related to the Goldbach conjecture and additive number theory.
How to Use
Enter a prime:
- Test: Is it a Stern prime?
- Decompositions: Show q+2ab forms
- Known list: All known Sterns
Rarity
As primes grow, they become easier to decompose as q+2ab. Most large primes have MANY such representations. Stern primes resist ALL of them — an increasingly rare property. The conjecture says this becomes impossible beyond some bound.
Connections
Related to Goldbach: if every even number ≥4 is a sum of two primes, then for p=q+2ab, we need q prime and 2ab even. Stern primes are the 'hardest' primes for this kind of additive decomposition.
Step-by-Step Instructions
- 1Enter prime.
- 2Check all q+2ab.
- 3Determine Stern.
- 4View known list.
- 5See statistics.