Prime Popular Books
Prime Biography & Facts
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is 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, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. 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 that is 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 {\displaystyle n} , called trial division, tests whether n {\displaystyle n} is a multiple of any integer between 2 and n {\displaystyle {\sqrt {n}}} . Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error, and the AKS primality test, which always produces the correct answer in polynomial time but is too slow to be practical. Particularly fast methods are available for numbers of special forms, such as Mersenne numbers. As of December 2018 the largest known prime number is a Mersenne prime with 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 large 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 even integer greater than 2 can be expressed as the sum of two primes, and the twin prime conjecture, that there are infinitely many pairs of primes that differ by two. 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. Definition and examples A natural number (1, 2, 3, 4, 5, 6, etc.) is called a prime number (or a prime) 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 {\displaystyle n} is prime if n {\displaystyle 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 {\displaystyle n} dots into a rectangular grid that is more than one dot wide and more than one dot high. For example, among the numbers 1 through 6, the numbers 2, 3, and 5 are the prime numbers, as there are no other numbers that divide them evenly (without a remainder). 1 is not prime, as it is specifically excluded in the definition. 4 = 2 × 2 and 6 = 2 × 3 are both composite. The divisors of a natural number n {\displaystyle n} are the natural numbers that divide n {\displaystyle n} evenly. Every natural number has both 1 and itself as a divisor. If it has any other divisor, it cannot be prime. This leads to an equivalent definition of prime numbers: they are the numbers with exactly two positive divisors. Those two are 1 and the number itself. As 1 has only one divisor, itself, it is not prime by this definition. Yet another way to express the same thing is that a number n {\displaystyle n} is prime if it is greater than one and if none of the numbers 2 , 3 , … , n − 1 {\displaystyle 2,3,\dots ,n-1} divides n {\displaystyle n} evenly. The first 25 prime numbers (all the prime numbers less than 100) 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 (sequence A000040 in the OEIS). No even number n {\displaystyle n} greater than 2 is prime because any such number can be expressed as the product 2 × n / 2 {\displaystyle 2\times n/2} . Therefore, every prime number other than 2 is an odd number, and is called an odd prime. Similarly, 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 even, and decimal numbers that end in 0 or 5 are divisible by 5. The set of all primes is sometimes denoted by P {\displaystyle \mathbf {P} } (a boldface capital P) or by P {\displaystyle \mathbb {P} } (a blackboard bold capital P). History 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 study of prime numbers come from the ancient Greek mathematians, who called them prōtos arithmòs (πρῶτος ἀριθμὸς). Euclid's Elements (c. 300 BC) proves the infinitude of primes and the fundamental theorem of arithmetic, and 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 (Alhazen) found Wilson's theorem, characterizing the prime numbers as the numbers n {\displaystyle n} that evenly divide ( n − 1 ) ! + 1 {\displaystyle (n-1)!+1} . He also conjectured that all even perfect numbers come from Euclid's construction using Mersenne primes, but was unable to prove it. Another Islamic mathematician, Ibn al-Banna' al-Marrakushi, observed that the sieve of Era.... Discover the Prime popular books. Find the top 100 most popular Prime books.
Best Seller Prime Books of 2024
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The Dutch House
Ann PatchettPulitzer Prize Finalist | New York Times Bestseller | A Read with Jenna Today Show Book Club Pick | A New York Times Book Review Notable Book |...
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Sycamore Row
John Grisham#1 NEW YORK TIMES BESTSELLER John Grisham returns to the iconic setting of his first novel, A Time to Kill, as Jake Brigance finds himself embroiled in a controversial trial that ...
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Me Before You
Jojo MoyesFrom the #1 New York Times bestselling author of The Giver of Stars and the forthcoming Someone Else's Shoes, discover the love story that captured over 20 million hearts in Me Bef...
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The Tattooist of Auschwitz
Heather Morris#1 New York Times Bestseller and #1 International BestsellerSoon to be a Peacock Original SeriesThis beautiful, illuminating tale of hope and courage is based on in...
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One Day in December
Josie Silver#1 NEW YORK TIMES BESTSELLER “Get ready to be swept up in a whirlwind romance. It absolutely charmed me.”Reese Witherspoon (A Reese’s Book Club Pick) “The perfect book to get lost...
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Witness to a Trial
John GrishamA startling and original courtroom drama from New York Times #1 Best Seller John Grisham that is the prequel to his newest legal thriller, The Whistler. An Original EShort. A judge...
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The Good Daughter
Karin Slaughter“The Good Daughter is like Law and Order meets The Good Wife.” theSkimmThe stunning new novel from the New York Times bestselling author of Pieces of Her...
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Marketing In Less Than 1000 Words
Bear BurnsOver 50,000 downloads worldwide Finally. A book on marketing you can read in 15 minutes flat.In less than 1000 words we explain the major principles of successful marketing the m...
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Prime Time Murder
Brittany E. BrinegarShe's little. She's feisty. Spoiler alert, she's not the killer. Move to Hollywood. Catch her big break. Become a movie star. Nowhere on Becky Robinson's todo list does it say dis...
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The Girl on the Train
Paula HawkinsThe #1 New York Times bestseller, USA Today Book of the Year and now a major motion picture starring Emily Blunt. Rachel takes the same commuter train every morning and night....
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Prime
Bob ParisOne of the most celebrated fitness experts in the world, Bob Paris has a new lifechanging message for the millions of men over 40 who want to get in shape: It isn't too late! No in...
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Before We Were Yours
Lisa WingateTHE BLOCKBUSTER HITOver two million copies sold! A New York Times, USA Today, Wall Street Journal, and Publishers Weekly Bestseller“Poignant, engrossing.”People “Lisa Wingate take...
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The Kite Runner
Khaled HosseiniThe #1 New York Times bestselling novel beloved by millions of readers the world over.“A vivid and engaging story that reminds us how long his people [of Afghanistan] have been str...
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The Game
Neil StraussHidden somewhere, in nearly every major city in the world, is an underground seduction lair. And in these lairs, men trade the most devastatingly effective techniques ever invented...
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IOS Deployment Primer
Apple Inc.iOS is transforming the way people work. Whether you’re at a small, medium, or large organization, deploying and managing a large number of iOS devices, apps, and data can seem ove...
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The Help
Kathryn StockettThe #1 New York Times bestselling novel and basis for the Academy Awardwinning filma timeless and universal story about the lines we abide by, and the ones we don’tnominated as one...
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Dear Edward
Ann NapolitanoNEW YORK TIMES BESTSELLER READ WITH JENNA BOOK CLUB PICK AS FEATURED ON TODAY “Make sure you have tissues handy when you read [this] surefooted tearjerker” (NPR) a...
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A Raisin in the Sun
Lorraine Hansberry"Never before, in the entire history of the American theater, has so much of the truth of Black people's lives been seen on the stage," observed James Baldwin shortly before A Rais...
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Squeeze Me
Carl HiaasenNEW YORK TIMES BEST SELLER A hilarious novel of social and political intrigue, set against the glittering backdrop of Florida’s gold coast, from the author of Skinny Dip and ...
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And Then There Were None
Agatha ChristieA PBS Great American Read Top 100 Pick One of the most famous and beloved mysteries from the queen of suspense, Agatha Christie! More than 100 million copies sold and now a L...
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The Racketeer
John Grisham#1 NEW YORK TIMES BESTSELLER “The Racketeer is guilty of only one thing: keeping us engaged until the very last page.”USA Today In the history of the United States, only four act...
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On Mystic Lake
Kristin HannahNATIONAL BESTSELLER A poignant and tender story of love, loss, passion, and the fragile threads that bind families together from the author of The Nightingale. “A beautifully...
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The Reckoning
John Grisham#1 NEW YORK TIMES BESTSELLER John Grisham's most powerful, surprising, and suspenseful thriller yet “A murder mystery, a courtroom drama, a family saga.” USA Today...
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A Discovery of Witches
Deborah HarknessBook one of the New York Times bestselling All Souls series, from the author of The Black Bird Oracle.“A wonderfully imaginative grownup fantasy with all the magic of Harry Potter ...
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Razor Girl
Carl HiaasenThe new fulltilt, unstoppably hilarious and entertaining novel from the bestselling author of Skinny Dip and Bad MonkeyWhen Lane Coolman's car is bashed from behind on the roa...
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The Things We Cannot Say
Kelly RimmerThe New York Times bestsellerfor fans of All the Light We Cannot See!From the bestselling author of Truths I Never Told You, Before I Let You Go, and the The Warsaw Orphan, Ke...
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Angel Falls
Kristin HannahFrom the #1 New York Times bestselling author of The Four Winds, Angel Falls is “a tearjerker . . . about the triumphs of family” (Detroit Free Press).When Mikaela Campbell, belove...
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Maine
J. Courtney SullivanNEW YORK TIMES BESTSELLER The celebrated author of Commencement and The Engagements introduces four unforgettable women and the abiding, often irrational love that keeps them...
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A Thousand Splendid Suns
Khaled HosseiniPropelled by the same superb instinct for storytelling that made The Kite Runner a beloved classic, the #1 New York Times bestseller A Thousand Splendid Suns is at once an incredib...
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The Selection
Kiera CassFall in lovefrom the very beginning. Discover the first book in the captivating, #1 New York Times bestselling Selection series.This ebook edition contains an excerpt of Kiera Cass...
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Tom Lake
Ann Patchett#1 NEW YORK TIMES BESTSELLER A REESE’S BOOK CLUB PICKIn this beautiful and moving novel about family, love, and growing up, Ann Patchett once again proves hers...
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The Bean Trees
Barbara Kingsolver“The Bean Trees is the work of a visionary. . . . It leaves you openmouthed and smiling.” Los Angeles TimesA bestseller that has come to be regarded as an Ame...
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The Invention of Wings
Sue Monk KiddFrom the celebrated author of The Secret Life of Bees, a magnificent novel about two unforgettable American women Writing at the height of her narrative and imaginative gifts, ...
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Bad Monkey
Carl HiaasenA wickedly funny novel from the New York Times bestselling author of Squeeze Me in which the greedy, the corrupt, and the degraders of what’s left of pristine Floridanow, of the Ba...
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The Last Anniversary
Liane MoriartyFrom Liane Moriarty, author of the #1 New York Times bestsellers Big Little Lies and Truly Madly Guilty, comes an unforgettable novel defined by her signature sharp wit, paget...
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The Girl with the Dragon Tattoo
Stieg LarssonONE OF TIME MAGAZINE'S 100 BEST MYSTERY AND THRILLER BOOKS OF ALL TIME #1 NATIONAL BESTSELLER The thrilling first book in the Girl with the Dragon Tattoo ...
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A Visit from the Goon Squad
Jennifer EganNATIONAL BESTSELLER NATIONAL BOOK CRITICS CIRCLE WINNER With music pulsing on every page, this startling, exhilarating novel of selfdestruction and redemption "fea...
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The Secret Life of Bees
Sue Monk KiddThe multimillion bestselling novel about a young girl's journey towards healing and the transforming power of love, from the awardwinning author of The Invention of Wings and The B...
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Gray Mountain
John Grisham#1 NEW YORK TIMES BESTSELLER John Grisham has a new hero ... and she’s full of surprises. The year is 2008 and Samantha Kofer’s career at a huge Wall Street ...