Prime Number Theorem - meaning and definition. What is Prime Number Theorem
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What (who) is Prime Number Theorem - definition


Prime number theorem         
  • Plot of the function <math>\ \pi(x;4,3)-\pi(x;4,1) \ </math> for n&nbsp;≤&nbsp;30000
  • Li(''x'') − ''π''(''x'')}} switches sign infinitely many times.
  • Li(''x'')}} converges more quickly from below.
THEOREM IN NUMBER THEORY
Prime Number Theorem; Dusart's inequality; Distribution of prime numbers; The Prime Number Theorem; Distribution of primes; Prime number theorem for arithmetic progressions; Prime number race
In mathematics, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers. It formalizes the intuitive idea that primes become less common as they become larger by precisely quantifying the rate at which this occurs.
prime number theorem         
  • Plot of the function <math>\ \pi(x;4,3)-\pi(x;4,1) \ </math> for n&nbsp;≤&nbsp;30000
  • Li(''x'') − ''π''(''x'')}} switches sign infinitely many times.
  • Li(''x'')}} converges more quickly from below.
THEOREM IN NUMBER THEORY
Prime Number Theorem; Dusart's inequality; Distribution of prime numbers; The Prime Number Theorem; Distribution of primes; Prime number theorem for arithmetic progressions; Prime number race
<mathematics> The number of prime numbers less than x is about x/log(x). Here "is about" means that the ratio of the two things tends to 1 as x tends to infinity. This was first conjectured by Gauss in the early 19th century, and was proved (independently) by Hadamard and de la Vall'ee Poussin in 1896. Their proofs relied on complex analysis, but Erdos and Selberg later found an "elementary" proof. (1995-04-10)
prime         
  • The [[Gaussian prime]]s with norm less than 500
  • The small gear in this piece of farm equipment has 13 teeth, a prime number, and the middle gear has 21, relatively prime to 13
  • alt=Construction of a regular pentagon using straightedge and compass
  • relative error]] of <math>\tfrac{n}{\log n}</math> and the logarithmic integral <math>\operatorname{Li}(n)</math> as approximations to the [[prime-counting function]]. Both relative errors decrease to zero as <math>n</math> grows, but the convergence to zero is much more rapid for the logarithmic integral.
  • alt=Demonstration, with Cuisenaire rods, that 7 is prime, because none of 2, 3, 4, 5, or 6 divide it evenly
  • alt=The Rhind Mathematical Papyrus
  • alt=Plot of the absolute values of the zeta function
  • alt=Animation of the sieve of Eratosthenes
  • The connected sum of two prime knots
  • alt=The Ulam spiral
POSITIVE INTEGER WITH EXACTLY TWO DIVISORS, 1 AND ITSELF
Primes; Prime numbers; Prime factor; Primality; Prime Numbers; Prime factors; Odd prime; 1 no longer prime; Prime divisor; Prime numbers in nature; Even primes; Prime Number; Infinity of primes; Prime-Numbers; Euclidean prime number theorem; Table Of Primes List; Prime; Primalities; Prime-number; Uncompound number; Odd prime number; Ω(n); Primality of 1; A000040; 1 is not a prime number; Prime (number); Primenumber; Primality of one; Infinity of the primes; Draft:The first mathematical of the prime numbers; Draft:Integer X prime matrix; Prime (mathematics)
I. a.
1.
First, original, primitive, primal, primeval, primordial, pristine, aboriginal.
2.
Highest, chief, principal.
3.
Early, blooming.
4.
First-rate, capital, excellent.
II. n.
1.
Beginning, opening, first part, earliest stage, dawn, morning.
2.
Youth, spring of life, early days.
3.
Perfection, flower, greatest beauty, health, or strength, best days, cream.