01353nam a22001937a 4500 20240409081453.0 240409b |||||||| |||| 00| 0 eng d 0025-570X Cohen, Joel E. Generalizations of Bertrand’s Postulate to Sums of Any Number of Primes (Journal Article) Philadelphia, PA :Taylor & Francis Group , September 2023 428-432p. Mathematics Magazine Volume 96: Number 4, October 2023 ***______{For Hard Copy, Please visit Library.}________*** Abstract: In 1845, Bertrand conjectured what became known as Bertrand’s postulate or the Bertrand-Chebyshev theorem: twice and prime strictly exceeds the next prime. Surprisingly, a stronger statement seems not to be well-known: the sum of any two consecutive primes strictly exceeds the next prime, except for the only equality 2+3=5. Our main theorem is a much more general result, perhaps not previously noticed, that compares sums of any number of primes. We prove this result using only the prime number theorem. We also give some numerical results and unanswered questions. Bertrand conjecture | Bertrand’s postulate| Bertrand-Chebyshev theorem| prime number theorem https://doi.org/10.1080/0025570X.2023.2231336 PER 0 0 0 0 RIEBPL RIEBPL 2024-04-09 0 2024-04-09 08:15:00 2024-04-09 PER 45625 45624