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arxiv: 1307.4444 · v1 · pith:WA5Z64LOnew · submitted 2013-07-16 · 🧮 math.NT

Conjecture on the value of Pi(10²6), the number of primes less than 10²6

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keywords valuevaluesconjecturedfunctionsinterpolationslessnumberobtained
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Based on the first 25 known values of Pi(10^n), the number of primes less than 10^n, with n integer between 1 and 25, we propose a conjectured value range of Pi(10^26) calculated by using polynomial interpolations with two corrective functions obtained by Thiele interpolations on relative differences of exact and interpolated values of Pi(10^n). The conjectured range value is in agreement with values obtained by the Eulerian logarithmic integral and with the Riemann functions.

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