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Generalizations of Bertrand’s Postulate to Sums of Any Number of Primes (Journal Article)

By:

Cohen, Joel E

Material type: Text

TextSeries: Mathematics Magazine ; Volume 96: Number 4, October 2023Publication details: Philadelphia, PA :Taylor & Francis Group , September 2023Description: 428-432pISSN:

0025-570X

Subject(s):

Bertrand conjecture | Bertrand’s postulate| Bertrand-Chebyshev theorem| prime number theorem

Online resources:

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Contents:

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Summary: 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.

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Item type	Current library	Call number	Status	Date due	Barcode
Periodicals	RIE BPL Library		Not for loan

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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.

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Generalizations of Bertrand’s Postulate to Sums of Any Number of Primes (Journal Article)

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