Arithmetic functions | Prime numbers

Prime gap

A prime gap is the difference between two successive prime numbers. The n-th prime gap, denoted gn or g(pn) is the difference between the (n + 1)-th and then-th prime numbers, i.e. We have g1 = 1, g2 = g3 = 2, and g4 = 4. The sequence (gn) of prime gaps has been extensively studied; however, many questions and conjectures remain unanswered. The first 60 prime gaps are: 1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, 2, 4, 14, 4, 6, 2, 10, 2, 6, 6, 4, 6, 6, 2, 10, 2, 4, 2, 12, 12, 4, 2, 4, 6, 2, 10, 6, 6, 6, 2, 6, 4, 2, ... (sequence in the OEIS). By the definition of gn every prime can be written as (Wikipedia).

Prime gap
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From playlist Summer of Math Exposition Youtube Videos

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Prime Gaps As Large As You Want (and Larger!) // [NUMBER THEORY]

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From playlist Math Mini

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Prove that the gap of successive prime numbers can be arbitrarily large

A simple number theory proof problem regarding prime number distribution: Prove that the gap of successive prime numbers can be arbitrarily large Please Like, Share and Subscribe!

From playlist Elementary Number Theory

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Infinitely Large Prime Gaps!

Infinitely Large Prime Gaps! #mathclass #shorts Check out the main channel @polymathematic ! We currently cannot prove that there are infinitely many prime gaps of size 2 (also known as "twin primes"), though we certainly think that there are. But it turns out it's trivial to prove that

From playlist polymathematic #shorts

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How to find prime numbers #shorts

In this short we talk about finding prime numbers. Full video at https://youtu.be/CEyZRhi45pE

From playlist #shorts mathematicsonline

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Interesting Facts About the Last Digits of Prime Numbers

This video explains some interesting facts about the last digits of prime numbers.

From playlist Mathematics General Interest

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From playlist Number: Factors, Multiples & Primes

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Gaps between primes – James Maynard – ICM2018

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From playlist Number Theory

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Terence Tao - Large and Small Gaps in the Primes [2015]

Slides for this talk: https://drive.google.com/file/d/1Nkwt96VXvHZxCEGg5qlcgAXZFPLme_kq/view?usp=sharing Latinos in the Mathematical Sciences Conference 2015 APRIL 9 - 11, 2015 Large and small gaps in the primes Terence Tao University of California, Los Angeles (UCLA) There are many

From playlist Number Theory

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LATMATH: Terence Tao - "Large and Small Gaps in the Primes"

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From playlist Latin@s in the Mathematical Sciences 2015

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Large Gaps between Primes - Numberphile

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From playlist James Maynard on Numberphile

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Twin Prime Conjecture - Numberphile

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James Maynard: Large gaps between primes in subsets

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From playlist Number Theory

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János Pintz: Polignac numbers and the consecutive gaps between primes

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From playlist Number Theory

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Almost Primes in Short Intervals

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From playlist Introduction to number theory (Berkeley Math 115)

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Encoding with Prime Numbers and Second Ratios - #MegaFavNumbers

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Related pages

Probable prime | Multiplicative function | Elliott–Halberstam conjecture | Riemann hypothesis | Prime-counting function | Big O notation | Product (mathematics) | Oppermann's conjecture | Gaussian moat | Hans Heilbronn | Robert Alexander Rankin | Twin prime conjecture | Factorial | Bonse's inequality | Sequence | Twin prime | Andrica's conjecture | Polymath Project | Arithmetic function | Additive function | Cramér's conjecture | Riemann zeta function | Bertrand's postulate | Firoozbakht's conjecture | Prime number | Prime number theorem | Polignac's conjecture | Ratio | Natural logarithm | Paul Erdős | Albert Ingham | Legendre's conjecture | Lindelöf hypothesis