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Pierpont Prime
In number theory, a Pierpont prime is a prime number of the form 2^u\cdot 3^v + 1\, for some nonnegative integers and . That is, they are the prime numbers for which is 3-smooth. They are named after the mathematician James Pierpont, who used them to characterize the regular polygons that can be constructed using conic sections. The same characterization applies to polygons that can be constructed using ruler, compass, and angle trisector, or using paper folding. Except for 2 and the Fermat primes, every Pierpont prime must be 1 modulo 6. The first few Pierpont primes are: It has been conjectured that there are infinitely many Pierpont primes, but this remains unproven. Distribution A Pierpont prime with is of the form 2^u+1, and is therefore a Fermat prime (unless ). If is positive then must also be positive (because 3^v+1 would be an even number greater than 2 and therefore not prime), and therefore the non-Fermat Pierpont primes all have the form , when is a p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Pierpont (mathematician)
James P. Pierpont (June 16, 1866 – December 9, 1938) was an American mathematician born in Connecticut. Life His father Cornelius Pierpont was a wealthy New Haven businessman. He did undergraduate studies at Worcester Polytechnic Institute, initially in mechanical engineering, but turned to mathematics. He went to Europe after graduating in 1886. He studied in Berlin and later in Vienna. He prepared his Ph.D. at the University of Vienna under Leopold Gegenbauer and Gustav Ritter von Escherich. His thesis, defended in 1894, was entitled ''Zur Geschichte der Gleichung fünften Grades bis zum Jahre 1858''. After his defense, he returned to New Haven and was appointed as a lecturer at Yale University, where he would spend most of his career. In 1898, he became professor. Research Initially, his research dealt with the Galois theory of equations. The Pierpont primes are named after him, as he introduced them in 1895 in connection with a problem of constructing regular polyg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
37 (number)
37 (thirty-seven) is the natural number following 36 and preceding 38. In mathematics 37 is the 12th prime number, and the 3rd isolated prime without a twin prime. 37 is the first irregular prime with irregularity index of 1, where the smallest prime number with an irregularity index of 2 is the thirty-seventh prime number, 157. The smallest magic square, using only primes and 1, contains 37 as the value of its central cell: Its magic constant is 37 x 3 = 111, where 3 and 37 are the first and third base-ten unique primes (the second such prime is 11). 37 requires twenty-one steps to return to 1 in the Collatz problem, as do adjacent numbers 36 and 38. The two closest numbers to cycle through the elementary Collatz pathway are 5 and 32, whose sum is 37; also, the trajectories for 3 and 21 both require seven steps to reach 1. On the other hand, the first two integers that return 0 for the Mertens function ( 2 and 39) have a difference of 37, where the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conjecture
In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis or Fermat's conjecture (now a theorem, proven in 1995 by Andrew Wiles), have shaped much of mathematical history as new areas of mathematics are developed in order to prove them. Resolution of conjectures Proof Formal mathematics is based on ''provable'' truth. In mathematics, any number of cases supporting a universally quantified conjecture, no matter how large, is insufficient for establishing the conjecture's veracity, since a single counterexample could immediately bring down the conjecture. Mathematical journals sometimes publish the minor results of research teams having extended the search for a counterexample farther than previously done. For instance, the Collatz conjecture, which concerns whether or not certain sequences of integers terminate, has been tested for all integers up to 1.2 × 101 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Andrew M
Andrew is the English form of the given name, common in many countries. The word is derived from the , ''Andreas'', itself related to ''aner/andros'', "man" (as opposed to "woman"), thus meaning "manly" and, as consequence, "brave", "strong", "courageous", and "warrior". In the King James Bible, the Greek "Ἀνδρέας" is translated as Andrew. Popularity In the 1990s, it was among the top ten most popular names given to boys in English-speaking countries. Australia In 2000, the name Andrew was the second most popular name in Australia after James. In 1999, it was the 19th most common name, while in 1940, it was the 31st most common name. Andrew was the first most popular name given to boys in the Northern Territory in 2003 to 2015 and continuing. In Victoria, Andrew was the first most popular name for a boy in the 1970s. Canada Andrew was the 20th most popular name chosen for male infants in 2005. Andrew was the 16th most popular name for infants in British Columbia i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mersenne Prime
In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century. If is a composite number then so is . Therefore, an equivalent definition of the Mersenne primes is that they are the prime numbers of the form for some prime . The exponents which give Mersenne primes are 2, 3, 5, 7, 13, 17, 19, 31, ... and the resulting Mersenne primes are 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, ... . Numbers of the form without the primality requirement may be called Mersenne numbers. Sometimes, however, Mersenne numbers are defined to have the additional requirement that should be prime. The smallest composite Mersenne number with prime exponent ''n'' is . Mersenne primes were studied in antiquity because of their close connection to perfect numbers: the Euclid–Eule ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierpont Exponent Distribution
Pierpont may refer to: Surname * Francis Harrison Pierpont (1814–1899), Governor of Virginia * Harry Pierpont (1902–1934), Prohibition-era gangster * James Pierpont (minister) (1659–1714), founder of Yale University * James Lord Pierpont (1822–1893), musician and soldier * James Pierpont (mathematician) (1866–1938), American mathematician * John Pierpont (1785–1866), American poet, teacher, lawyer, merchant, and minister * Lena Pierpont (1883–1958), Prohibition-era figure * Pierpont (Australian Financial Review) (born 1937), alter-ego of Trevor Sykes, financial journalist Middle name * John Pierpont Morgan (1837–1913), American financier and banker * John Pierpont Morgan, Jr. (1867–1943), American banker, finance executive, and philanthropist * Samuel Pierpont Langley (1834–1906), American astronomer, and physicist, inventor Places in the United States * Pierpont, South Dakota * Pierpont, Ohio * Pierpont Township, Ashtabula County, Ohio * Pierpont, Missouri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Even Number
In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is divisible by 2, and odd if it is not.. For example, −4, 0, and 82 are even numbers, while −3, 5, 23, and 69 are odd numbers. The above definition of parity applies only to integer numbers, hence it cannot be applied to numbers with decimals or fractions like 1/2 or 4.6978. See the section "Higher mathematics" below for some extensions of the notion of parity to a larger class of "numbers" or in other more general settings. Even and odd numbers have opposite parities, e.g., 22 (even number) and 13 (odd number) have opposite parities. In particular, the parity of zero is even. Any two consecutive integers have opposite parity. A number (i.e., integer) expressed in the decimal numeral system is even or odd according to whether its last digit is even or odd. That is, if the last digit is 1, 3, 5, 7, or 9, then it is odd; otherwise it is even—as the last digit of any ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Positive Number
In mathematics, the sign of a real number is its property of being either positive, negative, or 0. Depending on local conventions, zero may be considered as having its own unique sign, having no sign, or having both positive and negative sign. In some contexts, it makes sense to distinguish between a positive and a negative zero. In mathematics and physics, the phrase "change of sign" is associated with exchanging an object for its additive inverse (multiplication with −1, negation), an operation which is not restricted to real numbers. It applies among other objects to vectors, matrices, and complex numbers, which are not prescribed to be only either positive, negative, or zero. The word "sign" is also often used to indicate binary aspects of mathematical or scientific objects, such as odd and even ( sign of a permutation), sense of orientation or rotation ( cw/ccw), one sided limits, and other concepts described in below. Sign of a number Numbers from various number ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
433 (number)
400 (four hundred) is the natural number following 399 and preceding 401. Mathematical properties A circle is divided into 400 grads. Integers from 401 to 499 400s 401 401 is a prime number, tetranacci number, Chen prime, prime index prime * Eisenstein prime with no imaginary part * Sum of seven consecutive primes (43 + 47 + 53 + 59 + 61 + 67 + 71) * Sum of nine consecutive primes (29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61) * Mertens function returns 0, * Member of the Mian–Chowla sequence. 402 402 = 2 × 3 × 67, sphenic number, nontotient, Harshad number, number of graphs with 8 nodes and 9 edges * HTTP status code for "Payment Required". *The area code for Nebraska. 403 403 = 13 × 31, heptagonal number, Mertens function returns 0. * First number that is the product of an emirp pair. * HTTP 403, the status code for "Forbidden" * Also in the name of a retirement plan in the United States, 403(b). * The area code for southern Alberta. 404 40 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
257 (number)
257 (two hundred ndfifty-seven) is the natural number following 256 and preceding 258. 257 is a prime number of the form 2^+1, specifically with ''n'' = 3, and therefore a Fermat prime. Thus, a regular polygon with 257 sides is constructible with compass and unmarked straightedge. It is currently the second largest known Fermat prime. Analogously, 257 is the third Sierpinski prime of the first kind, of the form n^ + 1 ➜ 4^ + 1 = 257. It is also a balanced prime, an irregular prime, a prime that is one more than a square, and a Jacobsthal–Lucas number. Four-fold 257 is 1028, which is the prime index of the fifth Mersenne prime In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 1 ..., 8191. There are exactly 257 combinatorially distinct convex polyhedra with eight ver ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
193 (number)
193 (one hundred ndninety-three) is the natural number following 192 and preceding 194. In mathematics 193 is the number of compositions of 14 into distinct parts. In decimal, it is the seventeenth full repetend prime, or ''long prime''. * It is the only odd prime p known for which 2 is not a primitive root of 4p^2 + 1. * It is the thirteenth Pierpont prime, which implies that a regular 193-gon can be constructed using a compass, straightedge, and angle trisector. * It is part of the fourteenth pair of twin primes (191, 193), the seventh trio of prime triplets (193, 197, 199), and the fourth set of prime quadruplets (191, 193, 197, 199). Aside from itself, the '' friendly giant'' (the largest sporadic group) holds a total of 193 conjugacy classes. It also holds at least 44 maximal subgroups aside from the double cover of \mathbb (the forty-fourth prime number is 193). 193 is also the eighth numerator of convergents to Euler's number; correct to three decimal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
163 (number)
163 (one hundred ndsixty-three) is the natural number following 162 and preceding 164. In mathematics 163 is the 38th prime number and a strong prime in the sense that it is greater than the arithmetic mean of its two neighboring primes. 163 is a lucky prime and a fortunate number. 163 is a strictly non-palindromic number, since it is not palindromic in any base between base 2 and base 161. Given 163, the Mertens function returns 0, it is the fourth prime with this property, the first three such primes are 2, 101 and 149. As approximations, \pi \approx \approx 3.1411..., and e \approx \approx 2.7166\dots 163 is a permutable prime in base 12, which it is written as 117, the permutations of its digits are 171 and 711, the two numbers in base 12 are 229 and 1021 in base 10, both of which are prime. The function f(n) = n^2 - n + 41 gives prime values for all values of n between 0 and 39, while for n < 3000 approximately half of all values are prime. 163 ap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
