Brun’s Constant
Description of constant
$C_{81a}$, Brun’s Constant, is the sum of the reciprocals of the twin primes.
Known upper bounds
| Bound | Reference | Comments |
|---|---|---|
| 2.175398 | [K2007] | |
| 2.288513 | [PT2018] |
Known lower bounds
| Bound | Reference | Comments |
|---|---|---|
| 1.8267324395006 | [N1995] | Led to the discovery of the Pentium FDIV bug. |
| 1.83180806343237901198 | [N2010] | |
| 1.840503 | [PT2018] |
Additional comments and links
- Similar constants exist for other prime families, e.g., cousin primes.
- Wikipedia page on Brun’s theorem
References
- [K2007] Klyve, Dominic. Explicit Bounds on Twin Primes and Brun’s Constant.
- [N1995] Nicely, Thomas. Enumeration to 1e14 of the twin primes and Brun’s constant.
- [N2010] Nicely, Thomas. Enumeration of the twin-prime pairs from 1e16 to 2e16.
- [PT2018] Platt, Dave and Trudgian, Tim. Improved bounds on Brun’s constant.