TY - JOUR

T1 - Iterated absolute values of differences of consecutive primes

AU - Odlyzko, Andrew M.

N1 - Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.

PY - 1993/7

Y1 - 1993/7

N2 - Let dç, (n) = p„, the nth prime, for n > 1, and let dk+x(n) = \dk(n) - dk(n + 1) for k > 0, n > 1. A well-known conjecture, usually ascribed to Gilbreath but actually due to Proth in the 19th century, says that dk(\) = 1 for all k > 1. This paper reports on a computation that verified this conjecture for k < tt(1013) » 3 x 10". It also discusses the evidence and the heuristics about this conjecture. It is very likely that similar conjectures are also valid for many other integer sequences.

AB - Let dç, (n) = p„, the nth prime, for n > 1, and let dk+x(n) = \dk(n) - dk(n + 1) for k > 0, n > 1. A well-known conjecture, usually ascribed to Gilbreath but actually due to Proth in the 19th century, says that dk(\) = 1 for all k > 1. This paper reports on a computation that verified this conjecture for k < tt(1013) » 3 x 10". It also discusses the evidence and the heuristics about this conjecture. It is very likely that similar conjectures are also valid for many other integer sequences.

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U2 - 10.1090/S0025-5718-1993-1182247-7

DO - 10.1090/S0025-5718-1993-1182247-7

M3 - Article

AN - SCOPUS:84966258834

SN - 0025-5718

VL - 61

SP - 373

EP - 380

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 203

ER -