The greatest prime divisor of an arithmetic sequence (Q923615)
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scientific article; zbMATH DE number 4171043
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The greatest prime divisor of an arithmetic sequence |
scientific article; zbMATH DE number 4171043 |
Statements
The greatest prime divisor of an arithmetic sequence (English)
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1989
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Let \(1<c<3/2\) be fixed. It is shown that there are numbers with a large prime factor in the sequence \([n^ c]\). When c is close to 1 there are, in fact, primes in this sequence. [For the best result of this type see \textit{G. Kolesnik}, Pac. J. Math. 118, 437-447 (1985; Zbl 0571.10037)]. The proof is straightforward and improvements seem quite possible.
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prime like numbers
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large prime factors
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0.7985406517982483
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0.780518114566803
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0.7617459297180176
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