Abstract
Enumeration of the primes with difference 4 between consecutive primes, is counted up to 5×1010, yielding the counting function π2,4(5 × 1010) = 118905303. The sum of reciprocals of primes with gap 4 between consecutive primes is computedB 4(5×1010)=1.197054473029 andB 4=1.197054±7×10−6. And Enumeration of the primes with difference 6 between consecutive primes, is counted up to 5×1010, yielding the counting function π2,6(5 × 1010) = 215868063. The sum of reciprocals of primes with gap 6 between consecutive primes is computedB 6(5×1010)=0.93087506039231 andB 6=1.135835±1.2×10−6.
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Yeonyong Park received his Ph. D at KAIST under the direction of Hong Oh Kim. Since 1992 he has been at the Mokpo National University as a faculty. His research interests focus on the theory of harmonic analysis and the computation of gaps of the prime number.
Heonsoo Lee received his Ph.D at Mokpo national university under the direction of Yeonyong Park. Since 2003 he has been at the Mokpo National University as a lecturer. His research interests focus on the theory of the computation of gaps of the prime number.
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Park, Y., Lee, H. On the several differences between primes. JAMC 13, 37–51 (2003). https://doi.org/10.1007/BF02936073
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DOI: https://doi.org/10.1007/BF02936073