Cohen, Joel E.  <br/><br/>
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 .
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<br/><br/> 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. 
<br/><br/><label>ISSN: </label>0025-570X   
<br/><br/><label>Subjects--Topical Terms: </label><br/>Bertrand conjecture | Bertrand’s postulate| Bertrand-Chebyshev theorem| prime number theorem