selberg sieve
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2017 ◽  
Vol 68 (1) ◽  
pp. 169-193 ◽  
Author(s):  
Akshaa Vatwani
Keyword(s):  

2017 ◽  
Vol 57 (2) ◽  
pp. 151-184 ◽  
Author(s):  
M. Ram Murty ◽  
Akshaa Vatwani
Keyword(s):  

2011 ◽  
Vol 91 (3) ◽  
pp. 405-413 ◽  
Author(s):  
TERENCE TAO

AbstractWe show that for any fixed base a, a positive proportion of primes become composite after any one of their digits in the base a expansion is altered; the case where a=2 has already been established by Cohen and Selfridge [‘Not every number is the sum or difference of two prime powers’, Math. Comput.29 (1975), 79–81] and Sun [‘On integers not of the form ±pa±qb’, Proc. Amer. Math. Soc.128 (2000), 997–1002], using some covering congruence ideas of Erdős. Our method is slightly different, using a partially covering set of congruences followed by an application of the Selberg sieve upper bound. As a consequence, it is not always possible to test whether a number is prime from its base a expansion without reading all of its digits. We also present some slight generalisations of these results.


2006 ◽  
Vol 18 (1) ◽  
pp. 147-182 ◽  
Author(s):  
Ben Green ◽  
Terence Tao
Keyword(s):  

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