A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. A natural number greater than 1, not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 6 is composite because it is the product of two numbers that are both smaller than 6. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes, unique up to their order; the property of being prime is called primality. A simple but slow method of checking the primality of a given number n, called trial division, tests whether n is a multiple of any integer between 2 and n. Faster algorithms include the Miller–Rabin primality test, fast but has a small chance of error, the AKS primality test, which always produces the correct answer in polynomial time but is too slow to be practical.
Fast methods are available for numbers of special forms, such as Mersenne numbers. As of December 2018 the largest known prime number has 24,862,048 decimal digits. There are infinitely many primes, as demonstrated by Euclid around 300 BC. No known simple formula separates prime numbers from composite numbers. However, the distribution of primes within the natural numbers in the large can be statistically modelled; the first result in that direction is the prime number theorem, proven at the end of the 19th century, which says that the probability of a randomly chosen number being prime is inversely proportional to its number of digits, that is, to its logarithm. Several historical questions regarding prime numbers are still unsolved; these include Goldbach's conjecture, that every integer greater than 2 can be expressed as the sum of two primes, the twin prime conjecture, that there are infinitely many pairs of primes having just one number between them. Such questions spurred the development of various branches of number theory, focusing on analytic or algebraic aspects of numbers.
Primes are used in several routines in information technology, such as public-key cryptography, which relies on the difficulty of factoring large numbers into their prime factors. In abstract algebra, objects that behave in a generalized way like prime numbers include prime elements and prime ideals. A natural number is called a prime number if it is greater than 1 and cannot be written as the product of two smaller natural numbers; the numbers greater than 1 that are not prime are called composite numbers. In other words, n is prime if n items cannot be divided up into smaller equal-size groups of more than one item, or if it is not possible to arrange n dots into a rectangular grid, more than one dot wide and more than one dot high. For example, among the numbers 1 through 6, the numbers 2, 3, 5 are the prime numbers, as there are no other numbers that divide them evenly. 1 is not prime, as it is excluded in the definition. 4 = 2 × 2 and 6 = 2 × 3 are both composite. The divisors of a natural number n are the natural numbers.
Every natural number has both itself as a divisor. If it has any other divisor, it cannot be prime; this idea leads to a different but equivalent definition of the primes: they are the numbers with two positive divisors, 1 and the number itself. Yet another way to express the same thing is that a number n is prime if it is greater than one and if none of the numbers 2, 3, …, n − 1 divides n evenly; the first 25 prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97. No number n greater than 2 is prime because any such number can be expressed as the product 2 × n / 2. Therefore, every prime number other than 2 is an odd number, is called an odd prime; when written in the usual decimal system, all prime numbers larger than 5 end in 1, 3, 7, or 9. The numbers that end with other digits are all composite: decimal numbers that end in 0, 2, 4, 6, or 8 are and decimal numbers that end in 0 or 5 are divisible by 5; the set of all primes is sometimes denoted by P or by P.
The Rhind Mathematical Papyrus, from around 1550 BC, has Egyptian fraction expansions of different forms for prime and composite numbers. However, the earliest surviving records of the explicit study of prime numbers come from ancient Greek mathematics. Euclid's Elements proves the infinitude of primes and the fundamental theorem of arithmetic, shows how to construct a perfect number from a Mersenne prime. Another Greek invention, the Sieve of Eratosthenes, is still used to construct lists of primes. Around 1000 AD, the Islamic mathematician Ibn al-Haytham found Wilson's theorem, characterizing the prime numbers as the numbers n that evenly divide
Seraphim Falls is a 2006 American revisionist western film directed by television producer and director David Von Ancken in his first feature film. The storyline was conceived from a screenplay written by Abby Everett Jaques; the fictional story focuses on a bounty hunt for a Union soldier by a Confederate colonel following the American Civil War in the late 1860s. Pierce Brosnan, Liam Neeson, Michael Wincott, Tom Noonan, Ed Lauter star in principal roles. Seraphim Falls explores civil topics, such as human survival and war; the film was produced by the motion picture studio of Icon Productions. It was commercially distributed by Samuel Goldwyn Films and Destination Films theatrically, by Sony Pictures Home Entertainment for home media; the film score was composed by musician Harry Gregson-Williams, although a soundtrack version for the motion picture was not released to the public. Seraphim Falls premiered at the 2006 Toronto International Film Festival and was released to theaters in limited release in the United States on January 26, 2007 grossing $418,296 in domestic ticket sales.
It earned an additional $801,762 in box office business overseas for a combined worldwide total of $1,220,058 in revenue. The film was met with positive critical reviews before its initial screening in cinemas; the widescreen DVD edition of the film featuring scene selections and a bonus featurette, was released in the United States on May 15, 2007. Notable similarities have been found between the film and the 1976 revisionist western, The Outlaw Josey Wales directed by Clint Eastwood. In 1868, within the Ruby Mountains, Gideon roasts hare over an open fire. Gunshots ring out with one striking his left arm, he grabs. His attackers emerge from their cover to inspect his campsite. Colonel Morsman Carver, a former Confederate officer, is accompanied by Pope, Hayes and the Kid. After removing the bullet from his arm with his hunting knife at a secluded locale, Gideon leaves an open fire burning, which attracts the posse, he ends up killing Pope with his knife and ventures out again into the wilderness.
He attempts to steal a horse, but is caught by a young woman named Charlotte who helps him after she realizes he is injured. She redresses his wound and her family lets him sleep overnight in their farmhouse, he offers to buy their horse and leaves before daybreak. As the group of men approach Gideon's trail, he lays an ambush using a bear trap which impales the Kid, shot by Carver as an act of mercy. Parsons decides to leave the other men following the discovery of a dead bank robber, whom Gideon had killed earlier in an act of self-defense and whose bounty money exceeds Gideon's; as Parsons is preparing to load the dead body to take to Carson City for the reward money, Carver shoots the horse - which he declares is his, leaving Parsons to walk the 30 miles back to town carrying the body. Encountering a railroad under construction, Gideon steals some food; the foreman recognizes the stolen horse and detains Gideon. Carver and his remaining man, come upon the railroad site and search for Gideon.
Meanwhile, Gideon makes off with another horse. As Carver and Hayes draw closer, Gideon's horse can no longer take the strain of the heat and collapses. Gideon euthanizes the horse with his knife; when Carver and Hayes reach the horse's carcass, Hayes dismounts and marvels at what type of an animal would disembowel the creature. Gideon leaps out from the horse's belly, where he had been hiding, grabs Hayes threatening to kill him if Carver doesn't give up his gun. Carver instead shoots Hayes with his last bullet. Confronting each other and Gideon recall the events that put them at odds. After the end of the American Civil War, Gideon was ordered to track down former Confederate officers; when he arrived at Carver's home in Seraphim Falls to interrogate him, Carver was out in a nearby field. To coerce Carver's wife into revealing his whereabouts, believing that their house was empty, Gideon ordered their barn to be set on fire; the blaze spread to the house, as Carver returned from the cropland. While the soldiers restrained him, his wife and son ran inside the house to save their infant child, still in a bedroom.
Both men look on with horror at the unfolding tragedy. Gideon, racked with guilt over the tragedy, is seen dropping his gunbelt and walking away from his men; the two men fight, Gideon getting the better of Carver. He points Carver in the direction of a town and tells him that he will get nothing but torment if he continues his pursuit. Gideon sets off deeper into the countryside; when Carver catches up with Gideon, both men are on the brink of exhaustion. They confront each other again with their pistols. Gideon shoots Carver in the side but, instead of finishing him off, he offers himself to Carver. Carver decides not to throws his pistol aside. Gideon helps Carver to his feet and the two men walk into the distance away from one another. In a final scene, Gideon takes his knife, which he has used throughout the film, throws it into the ground. Liam Neeson as Colonel Morsman Carver: Like Brosnan, Neeson described being "kind of steeped in that western mythology growing up in Ireland." He likened his character, Carver, to Captain Ahab in Moby-Dick, "he's governed by this idea of revenge where he’s lost his humanity."
Holy Cross Church is a brick built parish church in Bieganowo, Kołaczkowo commune, in Września County, Poland. The church in Bieganowo was built around 1210. At that time it was a wooden temple, named "All Saints" church. In 1729 squire Franciszek Kowalski crest of Korab, began to build a new church, because the previous one was in ruins. In 1731 Bishop Jan Tarło of Poznan consecrated it; the church is first mentioned in 1737 by the archdeacon of Poznań, Kacykowski, "under the invocation of the Raising of the Holy Cross". However, in documents from the second visitation conducted by the Bishop Franciszek Ksawery de Wrbna Rydzyński in 1777, the temple was named "Finding of the Holy Cross". By 1799 the temple was again in ruins. Parish priest Mateusz Borowicz, working with the parish patron Jan Bronisz and parishioners rebuilt the entire church, with a new tower, a stone wall on the outside and a wooden interior. In 1926 the interior of the church was renovated by Edward Grabski. During the Nazi occupation the church was closed.
When the church was reopened after the war much of it had been destroyed by dry rot. On the night of 1 February 1982 at about 11:45PM a fire broke out and the building burned down in about 30 minutes. Only the tower survived. With the consent of church and state, the liturgy was held in the common rooms of the local, state-owned farms until 17 July 1982. On 15 March 1982, construction of the new church began, made possible by the work of parishioners, with help from State Farm director Bogumił Paul; the church was given new foundations and the original tower was restored. On 21 April 1982 Bishop Józef Glemp, who became the Polish Primate, assisted by bishop Jan Czerniak, laid the foundation stone along with a brass tube containing documents. By 17 July 1982 the church was completed and, on 25 June 1984, Glemp consecrated the church. In the tower behind the memorial tablet of 1982 are the entombed remains of Fr. Stanislaw Musial, murdered in Dachau concentration camp in 1940 and whose body was returned to his family by the Nazis.
Chronicle of the parish church of the Holy Cross in Bieganowo in Polish. Information about Holy Cross Church in Bieganowo Parish Bieganowo