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  • M2
    | number= 7
    193 bytes (19 words) - 13:43, 17 February 2019
  • M3
    | number= 31
    194 bytes (19 words) - 13:43, 17 February 2019
  • M4
    | number= 127
    195 bytes (19 words) - 13:44, 17 February 2019
  • M5
    | number= 8191
    204 bytes (18 words) - 13:46, 17 February 2019
  • Perfect number
    In [[mathematics]], a '''perfect number''' is defined as an integer which is the sum of its proper positive divisor ...and 3 are its proper positive divisors and 1 + 2 + 3 = 6. The next perfect number is 28 = 1 + 2 + 4 + 7 + 14. The next perfect numbers are 496 and 8128.
    6 KB (885 words) - 11:33, 7 March 2019
  • M9
    | number=2305843009213693951 ...l factoring]]. Pervushin used the [[Lucas-Lehmer test]] to prove that this number is prime.
    2 KB (213 words) - 14:30, 17 February 2019
  • Double check
    *human error (entering wrong number to test, misreading data, etc.) ...t]] does a verfication on all [[factor]]s reported. (It is easy to check a number for a single factor.)
    2 KB (373 words) - 15:08, 5 June 2019
  • Residue
    ...umber is exactly divisible. For the L-L test a zero residue means that the number is [[prime]].
    1 KB (235 words) - 10:24, 6 February 2019
  • GIMPS clients
    So, to test a number efficiently, one must apply the theory to get the tests down to the "weeks" ...came popular among PC enthusiasts and [[Overclocking|overclockers]] as its number-crunching algorithms exercise the computer's processor and memory to their
    8 KB (1,218 words) - 15:37, 13 August 2020
  • Mfaktc
    ...ics cards, this is a very fast program. The name mfaktc is "'''M'''ersenne number '''fakt'''oring with '''C'''UDA", it is a mixture of English with the Germa
    5 KB (765 words) - 14:54, 25 February 2019
  • Mfakto
    ...akt'''oring with '''o'''penCL) is a port of ''[[mfaktc]]'' ('''m'''ersenne number '''fakt'''oring with '''C'''UDA) (for use on ATI/AMD GPUs rather than NVIDI -d <xy> use OpenCL platform number x and device number y
    17 KB (2,524 words) - 12:39, 24 January 2019
  • Rho factorization method
    The idea is to create a sequence iterating a polynomial modulo the number to be factored. ...nvented by Richard Brent in 1980 who used it to factor the eighth [[Fermat number]].
    3 KB (558 words) - 10:28, 6 February 2019
  • Riesel number
    ...value of ''k'' such that {{Kbn|k|n}} is always composite for all [[natural number]]s. In order to demonstrate whether 509203 is the smallest Riesel number or not (the '''[[Riesel problem 1]]'''), a [[distributed computing project]
    827 bytes (112 words) - 08:21, 25 March 2024
  • M12
    | number=170141183460...715884105727 ...d why this happened. Lucas was following a sequence (see [[Double Mersenne number]]). The first possible Mersenne prime (2<sup>1</sup>-1=2), when placed back
    2 KB (354 words) - 14:52, 19 September 2021
  • Primality test
    ...er a given number is [[prime]] or [[composite number|composite]]. When the number is declared composite, the algorithm does not reveal the prime [[factor]]s. ...(which is far slower than a probable primality test except when the input number has a special form) is run on it.
    3 KB (501 words) - 05:20, 3 August 2021
  • Lucas primality test
    ...ality test''' invented in 1891 by [[Édouard Lucas]], determines whether a number N is prime or not, using the complete factorization of N-1.
    1 KB (177 words) - 14:31, 17 February 2019
  • Square root
    ...e non-negative real number whose ''square'' (the result of multiplying the number by itself) is <math>x</math>. ...real numbers, the concept of [[imaginary number|imaginary]] and [[complex number]]s has been developed to provide a mathematical framework to deal with the
    13 KB (1,873 words) - 16:52, 24 October 2020
  • Primality testing program
    | [[Mersenne number]]s<br/>a &times; b<sup>n</sup>±c (only factoring and [[probable prime|PRP] | [[generalized Fermat number]]s
    2 KB (314 words) - 21:23, 29 August 2019
  • Pépin's test
    '''Pépin's test''' is mainly used for proving the primality of [[Fermat number]]s, but it is of no help for finding the factors of such numbers. ...for proving the primality of other numbers, like the [[Generalized Fermat number]]s <math>F_{n,2} = 4^{3^n}+2^{3^n}+1</math> with k = 5 instead of k = 3.
    2 KB (401 words) - 14:40, 6 March 2019
  • Proof by induction
    ...= F<sub>n-1</sub> + F<sub>n-2</sub> and <math>\phi </math> = 1.61803... a number such that <math>\phi^2 = \phi + 1</math>.
    4 KB (679 words) - 13:57, 20 February 2019
  • Mprime (Cray)
    ...id Slowinski]] (later versions with [[Paul Gage]]), for testing [[Mersenne number]]s for [[Prime|primality]] on [[Cray Research|Cray]] [[Classes of computers
    639 bytes (92 words) - 12:02, 7 February 2019
  • Probable prime
    ...ecific conditions. While there may be probable primes that are [[Composite number|composite]] (called [[pseudoprime]]s), the condition is generally chosen in ...mality test (like [[Lucas-Lehmer test]]) will be needed to find out if the number is really composite or not.
    2 KB (232 words) - 07:28, 12 March 2024
  • Pseudoprime
    A '''pseudoprime''' is a [[composite number]] which passes some probabilistic [[primality test]]s. For example, a ''strong pseudoprime'' is a composite number that passes one iteration the [[Miller-Rabin pseudoprimality test]].
    1 KB (155 words) - 20:32, 25 July 2020
  • Floating-point
    ...onent]]. The [[base]] for the scaling is normally 2, 10 or 16. The typical number that can be represented exactly is of the form: ...at is, it can be placed anywhere relative to the significant digits of the number. This position is indicated separately in the internal representation, and
    2 KB (294 words) - 22:56, 3 February 2019
  • Factor5
    ...actoring program|program]] that performs [[Trial factoring]] of [[Mersenne number]]s. It is capable of trial factoring very large numbers, many billions of d :"factor <exponent> <start_bit> <stop_bit> <number of threads to use>"
    1 KB (201 words) - 21:16, 25 January 2019
  • Complex number
    A '''complex number''' is defined as a pair of [[real number]]s <math>z = (x, y)</math> where the following operations are defined: ...mbers behaves as real numbers. That's why the first element of the complex number is known as the ''real part'' and the second element as the ''imaginary par
    2 KB (280 words) - 14:59, 26 March 2023
  • Luigi Morelli
    ...upporting [[Trial factoring|factorization]] of large (or small) [[Mersenne number]]s, he wrote the [[Factor5]] [[program]]. As of February 2011, he wrote som ...w [http://www.doublemersennes.org/ website] dealing with [[Double Mersenne number]]s.
    1 KB (154 words) - 01:15, 15 January 2024
  • Operation Billion Digits
    ...e also unfeasible because they require operations modulo the billion digit number. The only part of this project that can be undertaken today is [[trial fact ...er the starting one. If you want to do a bigger range, just input a higher number here (be aware that adding a bit depth takes twice the time than the previo
    6 KB (918 words) - 16:28, 24 July 2020
  • M37
    | number=127411683030...973024694271 ...[[Roland Clarkson]], using [[Prime95]] written by [[George Woltman]]. The number is [http://www.mersenneforum.org/txt/37.txt {{Num|909526}} decimal digits]
    877 bytes (111 words) - 11:04, 18 February 2019
  • GIMPS factoring and sieving
    ...a factor than to do the Lucas-Lehmer Test; in fact, over 60% of [[Mersenne number]]s with prime exponents are eliminated from consideration as possible prime ...given Mersenne number up to some predetermined size, usually a prescribed number of bits.
    6 KB (962 words) - 10:08, 7 March 2019
  • Quadratic residue
    In [[mathematics]], a number {{V|q}} is called a '''quadratic residue''' [[modular arithmetic|modulo]] { In effect, a quadratic residue modulo {{V|p}} is a number that has a [[Modular square root|square root]] in [[modular arithmetic]] wh
    823 bytes (117 words) - 20:11, 26 October 2020
  • Modular square root
    A '''modular square root''' <math>r</math> of an [[integer]] number <math>a</math> modulo an integer <math>m</math> greater than 1 is an intege ...o zero, there is only one modular square root, namely zero. Otherwise, the number of square roots can be two or zero depending on whether the argument is a [
    5 KB (726 words) - 10:38, 6 February 2019
  • Legendre symbol
    If <math>p</math> is an odd [[prime]] number and <math>a</math> is an [[integer]], then the Legendre symbol There are a number of useful properties of the Legendre symbol which can be used to speed up c
    2 KB (348 words) - 18:57, 28 September 2023
  • Law of quadratic reciprocity
    ...</math> is a [[quadratic residue]] or non-residue modulo another odd prime number <math>q</math> if we know whether <math>q</math> is a quadratic residue or
    1 KB (208 words) - 18:19, 2 October 2022
  • Non-negative
    ...integers from zero upwards, and the non-negative reals are all the [[real number]]s from zero upwards. All whole numbers are non-negative.
    421 bytes (66 words) - 22:51, 26 January 2019
  • Ten million digits
    After the discovery of [[M38]] (the first [[megaprime]] or [[prime]] number greater than 1 million [[decimal]] [[digit]]s) in June of 1999, the next [[ ...was found, [[M46]]. By the end of 2010, all exponents that would produce a number less than {{Num|10000000}} digits had been [[primality test|tested]] at lea
    979 bytes (146 words) - 14:23, 6 March 2019
  • Mmff
    ...man for [[trial factoring]] small [[Fermat number]]s and [[double Mersenne number]]s.
    355 bytes (45 words) - 00:00, 27 January 2019
  • Double Mersenne number
    ...ble Mersenne number''' is a number where the exponent is also a [[Mersenne number]] and usually a [[Mersenne prime]]. These are generally denoted as '''MM<su ...igit]]s long. [[Tony Forbes]] lead an effort to find a [[factor]] for this number. The search has included all '''''[[Value k|k]]''''' values up to {{Num|116
    4 KB (655 words) - 14:50, 19 September 2021
  • PSearch
    ! scope="col" | Number ...ate, it was the 15th largest prime number, and the 2nd largest Proth prime number.
    1 KB (182 words) - 08:17, 12 July 2020
  • P-1 factorization method
    Let ''p'' be a prime divisor of the number ''N'' to be factored. If we somehow find a multiple of ''p-1'' we will find ...e method proceeds to compute <math>a^E\,\pmod{N}</math> where ''N'' is the number to factor.
    5 KB (814 words) - 01:35, 12 March 2019
  • Brent-Suyama extension
    ...of prime powers less than B1. Then by [[Fermat's Little Theorem]], a prime number p | S-1 if p-1 | E. ...instead computes T=S<sup>(6k)<sup>e</sup>-1</sup>, where e is a small even number >2. (6k)<sup>e</sup>-1 = (6k-1)*(6k+1)*(a higher order polynomial in k). Th
    2 KB (421 words) - 11:51, 28 January 2019
  • Self-initializing quadratic sieve
    Let N be the number to be factored. This number must not be a perfect power. If somehow we find two integers X and Y such t ...hand side. A number is a square when all its prime factors appear an even number of times.
    10 KB (1,763 words) - 02:56, 12 March 2019
  • Special number field sieve
    {{Shortcut|SNFS|Special number field sieve: special-purpose [[factorization]] algorithm.}} ...(SNFS)''' is a special-purpose [[factorization]] algorithm. The [[general number field sieve]] (GNFS) was derived from it.
    1 KB (186 words) - 12:07, 19 February 2019
  • Lone Mersenne Hunters
    ...currently being assigned by [[PrimeNet]] in order to eliminate [[Mersenne number]]s as possible [[Mersenne prime]] candidates. This work is suited to older
    1 KB (213 words) - 09:58, 7 March 2019
  • Fermat pseudoprimality test
    where ''p'' is a [[prime]] number and ''a'' is not multiple of <math>p</math>. ...math>. If the result is not 1, the number must be composite. Otherwise the number is either a prime or a Fermat [[pseudoprime]] with respect to base <math>a<
    1 KB (164 words) - 10:56, 6 February 2019
  • Miller-Rabin pseudoprimality test
    ...primality, and <math>N = 2^n\,k + 1</math> where <math>k</math> is an odd number. ...ce is 1 but the previous is not 1 or -1, or the last member is not 1, the number is composite.
    3 KB (432 words) - 15:33, 28 January 2019
  • Generalized Fermat prime
    A '''generalized Fermat prime''' is a [[generalized Fermat number]] which is [[prime]]. ...s://primes.utm.edu/primes/search.php?Comment=Generalized+Fermat&OnList=yes&Number=10&Style=HTML Current Top10] largest generalized Fermat primes at Prime Pag
    372 bytes (49 words) - 13:35, 6 March 2019
  • Generalized Fermat number
    There are different kinds of '''generalized [[Fermat number]]s'''. :<math>F_{0,r}</math> generates the [[Mersenne number]]s.
    5 KB (774 words) - 07:39, 27 May 2024
  • M51
    | number=148894445742...325217902591 To confirm that there were no errors in the [[hardware]] or [[software]], the number had to be independently verified by running tests on various machines with
    2 KB (255 words) - 05:53, 21 July 2021
  • Patrick Laroche
    ...less than 4 months and on just his fourth try, he discovered the new prime number. By way of comparison, some GIMPS participants have searched for more than
    987 bytes (147 words) - 01:27, 15 January 2024
  • PrimeGrid
    ...ch|Fermat Divisor Search]]: searching for large prime divisors of [[Fermat number]]s. Completed April 2021.
    3 KB (458 words) - 10:28, 26 March 2024
  • Worktype
    ...nne primes have been missed, and lastly finding [[factor]]s for [[Mersenne number]]s). ...ber. A found factor will conclusively prove that the number is [[Composite number|composite]], which eliminates the need to run a [[primality test]].
    4 KB (603 words) - 02:31, 18 August 2019
  • FermatSearch
    ...' is a distributed computing project searching for [[factor]]s of [[Fermat number]]s.
    361 bytes (46 words) - 13:48, 29 January 2019
  • Sieve of Eratosthenes
    ...math>. If <math>a \leq \sqrt{N}</math>, then <math>N</math> is [[composite number|composite]]; otherwise it is prime. ...after that will be divisible by <math>2</math>, we cross out every second number; all such numbers are composite.
    4 KB (654 words) - 11:10, 6 February 2019
  • Aliquot sequence
    An '''aliquot sequence''' is a sequence of numbers generated from an initial number using the sigma <math>\sigma(n)</math> function. ...visors''' of the number, <math>n</math>, which are all the divisors of the number, excluding itself. Therefore, sequences are generated thusly:
    6 KB (914 words) - 19:49, 21 February 2023
  • Abundant number
    An '''abundant number''' is any number, '''''n''''', which has a [[sigma|sigma value]] greater than '''''2n'''''. ...bers increase the size of an [[aliquot sequence]] because when an abundant number occurs in a sequence, the next step is larger than the current step. Also,
    671 bytes (92 words) - 00:34, 30 January 2019
  • Prime
    A '''prime number''' (or only '''prime''') is an [[integer]] greater than 1 that is only divi ...r 1. In other words, Q = (2 x 3 x 4 x 5 ... x P) + 1. From the form of the number Q, it is obvious that no integer from 2 to P divides evenly into Q, because
    2 KB (447 words) - 00:22, 10 July 2023
  • Twin prime
    ...'twin prime''' is a [[prime|prime number]] that differs from another prime number by two, for example the twin prime pair (41, 43). ! Up to !! Number of pairs
    2 KB (255 words) - 06:08, 21 February 2023
  • Riesel Prime Search
    :# Low-weight {{Vk}}-values that produce a very small number of primes (opposite to (1) above)
    845 bytes (120 words) - 02:21, 1 May 2024
  • Preda Mihăilescu
    His research interests include primality proving ([[GIMPS]]), computational number theory, cryptology, biometry and complex and numerical analysis.
    877 bytes (110 words) - 00:02, 15 January 2024
  • Nomenclature and notation
    ==[[Mersenne number]]== Any number whether [[Composite number|composite]] or [[prime]] of the form <math>2^{x}-1</math>. For one of these
    3 KB (467 words) - 08:48, 15 May 2024
  • Computing power
    ...of number of [[Processor|cores]], cycles per second each core runs at, and number of [[double-precision]] (64 bit) FLOPS each core can ideally perform. Altho
    2 KB (258 words) - 08:40, 15 May 2024
  • Seventeen or Bust/Sieving
    Turn proth_sieve on. Input your starting number and the ending one. Just wait after that until it finishes.
    2 KB (363 words) - 13:41, 1 February 2019
  • Why participate in GIMPS?
    ...nts' approximately 300 BC. His goal was to characterize the even [[perfect number]]s (numbers like 6 and 28 who are equal to the sum of their aliquot divisor Much of elementary number theory was developed while deciding how to handle large numbers, how to cha
    7 KB (1,252 words) - 09:47, 7 March 2019
  • Sieving
    '''Sieving''' is an algorithm to discover [[smooth number]]s and [[prime]] numbers from a sequence of [[integer]]s much faster than [ The next step depends on whether we need to find prime number or smooth numbers.
    3 KB (521 words) - 11:14, 6 February 2019
  • Smooth number
    A '''smooth number''' is an [[integer]] whose [[prime]] [[factor]]s are less or equal to a pre If this bound is B, we can say that the number is B-smooth.
    436 bytes (63 words) - 21:36, 3 February 2019
  • Sieving program
    *[[MultiSieve]] (performing sieving of different kinds of number) http://home.roadrunner.com/~mrodenkirch/home/MultiSieve.html
    2 KB (220 words) - 11:42, 7 March 2019
  • NewPGen
    ...mentations, it is a lot better than performing [[trial factoring]] on each number in the set.
    3 KB (529 words) - 09:32, 7 March 2019
  • Sophie Germain prime
    A [[prime]] number {{V|p}} is called a '''Sophie Germain prime''' if 2{{V|p}}+1 is also prime.
    1 KB (171 words) - 04:26, 3 November 2020
  • M13
    | number=686479766013...291115057151
    419 bytes (48 words) - 14:50, 19 September 2021
  • M14
    | number=531137992816...219031728127
    420 bytes (48 words) - 14:49, 19 September 2021
  • M15
    | number=104079321946...703168729087
    430 bytes (49 words) - 14:49, 19 September 2021
  • M16
    | number=147597991521...686697771007
    431 bytes (49 words) - 14:49, 19 September 2021
  • M17
    | number=446087557183...418132836351
    431 bytes (49 words) - 14:49, 19 September 2021
  • M18
    | number=259117086013...362909315071
    415 bytes (47 words) - 22:26, 17 February 2019
  • M11
    | number=162259276829...578010288127
    412 bytes (47 words) - 14:23, 17 February 2019
  • M10
    | number=618970019642...137449562111
    403 bytes (44 words) - 13:54, 17 February 2019
  • Proth prime
    *[[Wikipedia:Proth number|Wikipedia]]
    656 bytes (91 words) - 07:02, 31 August 2020
  • Riesel prime
    *[[Wikipedia:Riesel number|Riesel number]]
    2 KB (280 words) - 00:37, 25 May 2024
  • Riesel Sieve
    ...oblem]] (which states that {{Vk}}=509203 is the smallest possible [[Riesel number]]). To do that, they have to find primes for all the remaining k values to
    2 KB (326 words) - 10:29, 26 March 2024
  • M26
    | number=402874115778...523779264511
    455 bytes (52 words) - 23:01, 17 February 2019
  • Floor function
    ...ience, the '''floor function''' is the function that takes as input a real number <math>x</math> and gives as output the greatest [[integer]] less than or eq
    813 bytes (111 words) - 16:56, 29 August 2022
  • Power of two
    A number is said to be a '''power of two''' when its [[factorization]] gives only tw
    839 bytes (127 words) - 11:38, 6 February 2019
  • Introductory stuff
    In mathematics, a '''Mersenne prime''' is a [[prime]] number that is one less than a [[power of two]]. For example, 3 = 4 - 1 = 2<sup>2< ...s of relatively small primes. Trial factoring discovers if there is such a number. If it is, the more expensive Lucas-Lehmer test isn't needed. This type of
    14 KB (2,370 words) - 15:15, 17 August 2019
  • What use are prime numbers anyway?
    ...Wikipedia:G. H. Hardy|Godfrey H. Hardy]] (1877 - 1947) said of his work in number theory :"Here is one science (number theory) at any rate whose very remoteness from ordinary human activities sh
    3 KB (497 words) - 07:17, 22 May 2020
  • Overclocking
    ...nd the processor speed. The reason for this, is so one board can operate a number of processors with different speed settings. ...nchmark. The benchmark is fairly diverse and allows the user to change the number of digits of PI that can be calculated from 16 Thousand to 32 Million. The
    14 KB (2,326 words) - 15:17, 11 February 2019
  • Triangular number
    ..." (because it is triangular) after a number) represents the summing of a number with all whole numbers smaller than it. *[[Wikipedia:Triangular_number|Triangular number]]
    655 bytes (81 words) - 12:49, 25 March 2019
  • Pocklington's theorem
    ...vented by H. C. Pocklington in 1914, which is a [[primality test]] for the number ''N'', states:
    2 KB (346 words) - 19:51, 30 August 2019
  • Multiple polynomial quadratic sieve
    Let <math>N</math> be the number to be factored. This number must not be a perfect power. If somehow we find two integers <math>X</math> ...hand side. A number is a square when all its prime factors appear an even number of times.
    6 KB (1,068 words) - 14:33, 13 February 2019
  • Proth number
    In [[number theory]], a '''Proth number''' is a number of the form A [[Proth prime]] is a Proth number, which is prime.
    670 bytes (104 words) - 10:59, 9 July 2021
  • 27121 Search
    ...tion system, which makes it easy to use [[PRPclient]] to reserve a testing number directly from [http://prpnet.primegrid.com:12006/ the website]. Then this application will use [[LLR]] or [[PFGW]] to test this testing number and afterwards submit the result back via the website.
    983 bytes (138 words) - 13:25, 8 February 2019
  • 12121 Search
    ...tion system, which makes it easy to use [[PRPclient]] to reserve a testing number directly from [http://prpnet.primegrid.com:12001/ the website]. Then this application will use [[LLR]] or [[PFGW]] to test this testing number and afterwards submit the result back via the website.
    984 bytes (143 words) - 13:30, 8 February 2019
  • Assignments
    where n is the number to reserve. Then, you must set the cache option to reflect the processing t ...as chosen arbitrarily. This is because the reported credit is cut off at a number of significant digits which lies in the range of the actual value for that
    20 KB (3,473 words) - 18:42, 14 December 2023
  • GIMPS type of work
    ==Factoring of a prime number (exponent) candidate== ...pically distributed 1-3 curves at a time from PrimeNet (one can change the number of curves by modifying [[Worktodo.txt]]). This is run on smaller exponents
    4 KB (757 words) - 15:17, 25 July 2020
  • GIMPS networking, PrimeNet and communication
    For nonet computers it is desirable to minimize the number of communication attempts. Set the send new end dates in options / preferen where you substitute the protocol, proxy server domain name and port number exactly as they appear in your web browser. You might need to remove the <c
    8 KB (1,269 words) - 10:09, 7 March 2019
  • GIMPS chances of finding a prime number
    ...are used to calculate the probability of something happening based on the number of possible outcomes, not on what the last three or three hundred outcomes ...your next throw are 1:6. What has happened in the past does not affect the number of faces on the dice, which is all that is used to calculate the odds.
    3 KB (593 words) - 10:09, 7 March 2019
  • Worktodo.txt
    :AdvancedTest simply [[Lucas-Lehmer test|LL]] tests the given [[Mersenne number]], (ignoring any sort of prefactoring) and is used by [[Prime95]] when you where k, b, n, c represent a number k &times; b<sup>n</sup> + c. (c can take negative values.)
    2 KB (273 words) - 22:58, 11 May 2019
  • Assignment ID
    ...ponent) PrimeNet will issue a 32 character hexadecimal assignment ID. This number appears to be random (at least in part), so an individual cannot construct
    837 bytes (127 words) - 08:43, 15 May 2024
  • Bit level
    Since [[Mersenne number]]s are by nature [[binary]], it makes sense to perform calculations on them ...mber binaries are twice as large, while decimals are ten times as large. A number that has 70 binary digits (all 1's) would be at the 70 bit level. To check
    1 KB (193 words) - 18:47, 14 December 2023
  • Triple check
    ...t match. If the residues match, then the number is known to be [[composite number|composite]], (this assumes that the residue is not zero, otherwise it is [[ ...ainst some error in either software or hardware design or manufacture, the number will be tested using [[Mlucas]] or [[Glucas]] on a computer using an Itaniu
    1 KB (181 words) - 14:37, 11 February 2019

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