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Mertens and conjecture
For example, the Mertens conjecture is a statement about natural numbers that is now known to be false, but no explicit counterexample ( i. e., a natural number n for which the Mertens function M ( n ) equals or exceeds the square root of n ) is known: all numbers less than 10 < sup > 14 </ sup > have the Mertens property, and the smallest number which does not have this property is only known to be less than the exponential of 1. 59 × 10 < sup > 40 </ sup >, which is approximately 10 to the power 4. 3 × 10 < sup > 39 </ sup >.
This hypothesis, known as Mertens conjecture, was disproved in 1985 by Andrew Odlyzko and Herman te Riele
In mathematics, the Mertens conjecture is the incorrect statement that the Mertens function M ( n ) is bounded by √ n, which implies the Riemann hypothesis.
where μ ( k ) is the Möbius function, then the Mertens conjecture is that for all n > 1,
# REDIRECT Mertens conjecture
Because the Möbius function only takes the values − 1, 0, and + 1, the Mertens function moves slowly and there is no n such that | M ( n )| > n. The Mertens conjecture went further, stating that there would be no n where the absolute value of the Mertens function exceeds the square root of n. The Mertens conjecture was proven false in 1985 by Andrew Odlyzko and Herman te Riele.
He is known, a. o., for proving the correctness of the Riemann hypothesis for the first 1. 5 billion non-trivial zeros of the Riemann zeta function, with Jan van de Lune and Dik Winter, for disproving the Mertens conjecture, with Andrew Odlyzko, and for factoring large numbers of world record size.
te Riele, " Disproof of the Mertens conjecture ", Journal für die reine und angewandte Mathematik 357 ( 1985 ), 138 – 160.

Mertens and concerning
A translation into English has been made by Silvanus P. Thompson (" Epistle of Peter Peregrinus of Maricourt, to Sygerus of Foucaucourt, Soldier, concerning the Magnet ", Chiswick Press, 1902 ); by Brother Arnold Charles Mertens (" The Letter of Petrus Peregrinus on the Magnet, A. D. 1269 ", with introductory note by Brother Potamian M. F. O ’ Reilly, York, 1904 ); and H. D. Harradon, (“ Some Early Contributions to the History of Geomagnetism-I ,” in Terrestrial Magnetism and Atmospheric Electricity Journal of Geophysical Research 48, 3-17 pp. 6 – 17 ).

Mertens and its
The Meissel – Mertens constant is analogous to the Euler – Mascheroni constant, but the harmonic series sum in its definition is only over the primes rather than over all integers and the logarithm is taken twice, not just once.
Despite its success, Frank Mertens left the band that year and was replaced in January 1985 by Ricky Echolette ( born Wolfgang Neuhaus, in Cologne on 7 August 1960 ), who was credited on the Afternoons in Utopia album.
Further still, the Mertens ' Water Monitor ( Water goanna – Varanus mertensi ), found in lagoons and rivers across northern Australia, is streamlined for swimming, using its tail as a paddle.

Mertens and growth
In a paper on the growth rate of the sum-of-divisors function published in 1983, Guy Robin proved that in Mertens ' 2nd theorem the difference

Mertens and bounded
After computing these values Mertens conjectured that the modulus of M ( n ) is always bounded by √ n.

Mertens and by
Carvings by famous names like Junghanel, Klaus Mertens, Karl, Olaf Kolbe, Petersen, Christian Ulbricht and especially the Steinbach nutcrackers have become collectors ' items.
Ola Toivonen opened the goal account by scoring a fine heel goal, and the victory was accordingly sealed by goals from Dries Mertens and Jeremain Lens.
The Town of Mertens is served by the Frost Independent School District.
* The Cello Suites of Bach: History-Analysis-Detailed Interpretation-Program Notes-Audio-Video-Comprehensive analysis and notes on interpretation by cellist Georg Mertens.
The Belly of an Architect is a 1987 film drama written and directed by Peter Greenaway, featuring original music by Glenn Branca and Wim Mertens.
A curious relation given by Mertens himself involving the second Chebyshev function is
355 = 5 × 71, Smith number, Mertens function returns 0, divisible by the number of primes below it.
With Mertens now filling the gap left by his departure, the band forged ahead with recording their follow-up single and debut album.
It was proved by Franz Mertens that if the series converges to B and the series converges absolutely to A then their Cauchy product converges to AB.
In number theory, Mertens ' theorems are three 1874 results related to the density of prime numbers proved by Franz Mertens
Notably, herpetologists Karl Schmidt and Robert Mertens were killed by a boomslang and twig snake, respectively, after each underestimated the effects of the bite and failed to seek medical help.
Vervoort was replaced by Linda Mertens.

Mertens and x
The Mertens function M ( x ) is the sum function for the Möbius function, in the theory of arithmetic functions.
No analog of the Skewes number ( an upper bound on the first natural number x for which π ( x ) > li ( x )) is known in the case of Mertens ' 2nd and 3rd theorems.

Mertens and <
3 < sup > 2 </ sup > × 37, Mertens function returns 0, Harshad number.
2 < sup > 2 </ sup > × 7 × 13, tetrahedral number, sum of twelve consecutive primes ( 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 ), Mertens function returns 0, nontotient, Harshad number.
404 = 2 < sup > 2 </ sup > × 101, Mertens function returns 0, nontotient, noncototient.
405 = 3 < sup > 4 </ sup > × 5, Mertens function returns 0, Harshad number ; HTTP error code for " Method not allowed ".
414 = 2 × 3 < sup > 2 </ sup > × 23, Mertens function returns 0, nontotient, Harshad number, HTTP error code for " Request URI too long ", Area code for Milwaukee, Wisconsin.
3 < sup > 2 </ sup > × 47, Mertens function returns 0, Harshad number
424 = 2 < sup > 3 </ sup > × 53, sum of ten consecutive primes ( 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 ), Mertens function returns 0, refactorable number, self number
2 < sup > 2 </ sup > × 107, Mertens function returns 0, nontotient
608 = 2 < sup > 5 </ sup > × 19, Mertens function ( 608 )
2 < sup > 2 </ sup > × 3 × 53, sum of ten consecutive primes ( 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 ), Smith number, Mertens function ( 636 )
7 < sup > 2 </ sup > × 13, Mertens function ( 637 ) = 0, decagonal number

Mertens and 1
1, Ton Koopman, Amsterdam Baroque Orchestra & Choir, Barbara Schlick, Kai Wessel, Guy de Mey, Klaus Mertens.
Google posted three bids based on mathematical numbers: $ 1, 902, 160, 540 ( Brun's constant ), $ 2, 614, 972, 128 ( Meissel – Mertens constant ), and $ 3. 14159 billion ( pi ).
1, Ton Koopman, Amsterdam Baroque Orchestra & Choir, Barbara Schlick, Kai Wessel, Guy de Mey, Klaus Mertens, Antoine Marchand 1994

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