Geodesic
Determining Mills' constant and a note on Honaker's problem
Journal of integer sequences, Tome 8 (2005) no. 4.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In 1947 Mills proved that there exists a constant $A$ such that $\lfloor A^{3^n} \rfloor$ is a prime for every positive integer $n$. Determining $A$ requires determining an effective Hoheisel type result on the primes in short intervals--though most books ignore this difficulty. Under the Riemann Hypothesis, we show that there exists at least one prime between every pair of consecutive cubes and determine (given RH) that the least possible value of Mills' constant $A$ does begin with $1.3063778838$. We calculate this value to $6850$ decimal places by determining the associated primes to over $6000$ digits and probable primes (PRPs) to over $60000$ digits. We also apply the Cramér-Granville Conjecture to Honaker's problem in a related context.
Classification : 11Y60, 11Y11, 11A41
Keywords: Mills constant, primes in short intervals, prime gaps, elliptic curve primality testing, cramér-granville conjecture, honaker's problem 
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     author = {Caldwell, Chris K. and Cheng, Yuanyou},
     title = {Determining {Mills'} constant and a note on {Honaker's} problem},
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     number = {4},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2005__8_4_a7/}
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Caldwell, Chris K.; Cheng, Yuanyou. Determining Mills' constant and a note on Honaker's problem. Journal of integer sequences, Tome 8 (2005) no. 4. http://geodesic.mathdoc.fr/item/JIS_2005__8_4_a7/