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  2. Particular values of the Riemann zeta function - Wikipedia

    en.wikipedia.org/wiki/Particular_values_of_the...

    Zeros of the Riemann zeta except negative even integers are called "nontrivial zeros". The Riemann hypothesis states that the real part of every nontrivial zero must be ⁠ 1 / 2 ⁠. In other words, all known nontrivial zeros of the Riemann zeta are of the form z = ⁠ 1 / 2 ⁠ + yi where y is a real number.

  3. Riemann hypothesis - Wikipedia

    en.wikipedia.org/wiki/Riemann_hypothesis

    The Riemann zeta function is defined for complex s with real part greater than 1 by the absolutely convergent infinite series = = = + + +Leonhard Euler considered this series in the 1730s for real values of s, in conjunction with his solution to the Basel problem.

  4. 68 (number) - Wikipedia

    en.wikipedia.org/wiki/68_(number)

    68 is a composite number; a square-prime, of the form (p 2, q) where q is a higher prime. It is the eighth of this form and the sixth of the form (2 2.q). 68 is a Perrin number. [1] It has an aliquot sum of 58 within an aliquot sequence of two composite numbers (68, 58,32,31,1,0) to the Prime in the 31-aliquot tree.

  5. List of types of numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_types_of_numbers

    Positive numbers: Real numbers that are greater than zero. Negative numbers: Real numbers that are less than zero. Because zero itself has no sign, neither the positive numbers nor the negative numbers include zero. When zero is a possibility, the following terms are often used: Non-negative numbers: Real numbers that are greater than or equal ...

  6. List of number fields with class number one - Wikipedia

    en.wikipedia.org/wiki/List_of_number_fields_with...

    All complex cubic fields with discriminant greater than −500 have class number one, except the fields with discriminants −283, −331 and −491 which have class number 2. The real root of the polynomial for −23 is the reciprocal of the plastic ratio (negated), while that for −31 is the reciprocal of the supergolden ratio. The ...

  7. Complex number - Wikipedia

    en.wikipedia.org/wiki/Complex_number

    A real number a can be regarded as a complex number a + 0i, whose imaginary part is 0. A purely imaginary number bi is a complex number 0 + bi, whose real part is zero. It is common to write a + 0i = a, 0 + bi = bi, and a + (−b)i = a − bi; for example, 3 + (−4)i = 3 − 4i.

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  9. Goldbach's conjecture - Wikipedia

    en.wikipedia.org/wiki/Goldbach's_conjecture

    In 1975, Hugh Lowell Montgomery and Bob Vaughan showed that "most" even numbers are expressible as the sum of two primes. More precisely, they showed that there exist positive constants c and C such that for all sufficiently large numbers N, every even number less than N is the sum of two primes, with at most CN 1 − c exceptions.