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  2. List of integer sequences - Wikipedia

    en.wikipedia.org/wiki/List_of_integer_sequences

    The smallest integer m > 1 such that p n # + m is a prime number, where the primorial p n # is the product of the first n prime numbers. A005235 Semiperfect numbers

  3. List of unsolved problems in mathematics - Wikipedia

    en.wikipedia.org/wiki/List_of_unsolved_problems...

    Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.

  4. Smale's problems - Wikipedia

    en.wikipedia.org/wiki/Smale's_problems

    Smale's problems is a list of eighteen unsolved problems in mathematics proposed by Steve Smale in 1998 [1] and republished in 1999. [2] Smale composed this list in reply to a request from Vladimir Arnold, then vice-president of the International Mathematical Union, who asked several mathematicians to propose a list of problems for the 21st century.

  5. On-Line Encyclopedia of Integer Sequences - Wikipedia

    en.wikipedia.org/wiki/On-Line_Encyclopedia_of...

    The On-Line Encyclopedia of Integer Sequences (OEIS) is an online database of integer sequences. It was created and maintained by Neil Sloane while researching at AT&T Labs . He transferred the intellectual property and hosting of the OEIS to the OEIS Foundation in 2009, [ 4 ] and is its chairman.

  6. Composition (combinatorics) - Wikipedia

    en.wikipedia.org/wiki/Composition_(combinatorics)

    Each positive integer n has 2 n−1 distinct compositions. Bijection between 3 bit binary numbers and compositions of 4. A weak composition of an integer n is similar to a composition of n, but allowing terms of the sequence to be zero: it is a way of writing n as the sum of a sequence of non-negative integers. As a consequence every positive ...

  7. Goldbach's conjecture - Wikipedia

    en.wikipedia.org/wiki/Goldbach's_conjecture

    The prime number theorem asserts that an integer m selected at random has roughly a ⁠ 1 / ln m ⁠ chance of being prime. Thus if n is a large even integer and m is a number between 3 and ⁠ n / 2 ⁠, then one might expect the probability of m and n − m simultaneously being prime to be ⁠ 1 / ln m ln(n − m) ⁠.

  8. Remainder - Wikipedia

    en.wikipedia.org/wiki/Remainder

    Given an integer a and a non-zero integer d, it can be shown that there exist unique integers q and r, such that a = qd + r and 0 ≤ r < | d |. The number q is called the quotient, while r is called the remainder. (For a proof of this result, see Euclidean division. For algorithms describing how to calculate the remainder, see division algorithm.)

  9. Millennium Prize Problems - Wikipedia

    en.wikipedia.org/wiki/Millennium_Prize_Problems

    The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved mathematical problems, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Riemann hypothesis, Yang–Mills existence and mass gap, and the Poincaré conjecture at the ...

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