Primes of the Form $m^2+1$ and Goldbach's `Other Other' Conjecture
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866929700087005184 |
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| author | Grantham, Jon Graves, Hester |
| author_facet | Grantham, Jon Graves, Hester |
| contents | We compute all primes up to $6.25\times 10^{28}$ of the form $m^2+1$. Calculations using this list verify, up to our bound, a less famous conjecture of Goldbach. We introduce `Goldbach champions' as part of the verification process and prove conditional results about them, assuming either Schinzel's Hypothesis H or the Bateman-Horn Conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03513 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Primes of the Form $m^2+1$ and Goldbach's `Other Other' Conjecture Grantham, Jon Graves, Hester Number Theory 11N32, 11P32 We compute all primes up to $6.25\times 10^{28}$ of the form $m^2+1$. Calculations using this list verify, up to our bound, a less famous conjecture of Goldbach. We introduce `Goldbach champions' as part of the verification process and prove conditional results about them, assuming either Schinzel's Hypothesis H or the Bateman-Horn Conjecture. |
| title | Primes of the Form $m^2+1$ and Goldbach's `Other Other' Conjecture |
| topic | Number Theory 11N32, 11P32 |
| url | https://arxiv.org/abs/2502.03513 |