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Good Prime
A good prime is a prime number whose square is greater than the product of any two primes at the same number of positions before and after it in the sequence of primes. That is, good prime satisfies the inequality :p_n^2 > p_ \cdot p_ for all 1 ≤ ''i'' ≤ ''n''−1, where ''pk'' is the ''k''th prime. Example: the first primes are 2, 3, 5, 7 and 11. Since for 5 both the conditions :5^2 >3 \cdot 7 :5^2 >2 \cdot 11 are fulfilled, 5 is a good prime. There are infinitely many good primes. The first good primes are: : 5, 11, 17, 29, 37, 41, 53, 59, 67, 71, 97, 101, 127, 149, 179, 191, 223, 227, 251, 257, 269, 307, 311, 331, 347, 419, 431, 541, 557, 563, 569, 587, 593, 599, 641, 727, 733, 739, 809, 821, 853, 929, 937, 967 . An alternative version takes only ''i'' = 1 in the definition. With that there are more good primes: : 5, 11, 17, 29, 37, 41, 53, 59, 67, 71, 79, 97, 101, 107, 127, 137, 149, 157, 163, 173, 179, 191, 197 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Number
A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), 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, or , 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 factorization, 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 primality test, method of checking the primality of a given number , called trial division, tests whether is a multiple of any integer between 2 and . Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
149 (number)
149 (one hundred [and] forty-nine) is the natural number between 148 (number), 148 and 150 (number), 150. In mathematics 149 is the 35th prime number, the first prime whose difference from the previous prime is exactly 10, an emirp, and an irregular prime. After 1 and 127, it is the third smallest de Polignac number, an odd number that cannot be represented as a prime plus a power of two. More strongly, after 1, it is the second smallest number that is not a sum of two prime powers. It is a tribonacci number, being the sum of the three preceding terms, 24, 44, 81. There are exactly 149 integer points in a closed circular disk of radius 7, and exactly 149 ways of placing six queens (the maximum possible) on a 5 × 5 chess board so that each queen attacks exactly one other. The barycentric subdivision of a tetrahedron produces an abstract simplicial complex with exactly 149 simplices. References External links {{DEFAULTSORT:149 (Number) Integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
431 (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] |
347 (number)
300 (three hundred) is the natural number following 299 and preceding 301. In Mathematics 300 is a composite number and the 24th triangular number. It is also a second hexagonal number. Integers from 301 to 399 300s 301 302 303 304 305 306 307 308 309 310s 310 311 312 313 314 315 315 = 32 × 5 × 7 = D_ \!, rencontres number, highly composite odd number, having 12 divisors. It is a Harshad number, as it is divisible by the sum of its digits. It is a Zuckerman number, as it is divisible by the product of its digits. 316 316 = 22 × 79, a centered triangular number and a centered heptagonal number. 317 317 is a prime number, Eisenstein prime with no imaginary part, Chen prime, one of the rare primes to be both right and left-truncatable, and a strictly non-palindromic number. 317 is the exponent (and number of ones) in the fourth base-10 repunit prime. 318 319 319 = 11 & ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
331 (number)
300 (three hundred) is the natural number following 299 and preceding 301. In Mathematics 300 is a composite number and the 24th triangular number. It is also a second hexagonal number. Integers from 301 to 399 300s 301 302 303 304 305 306 307 308 309 310s 310 311 312 313 314 315 315 = 32 × 5 × 7 = D_ \!, rencontres number, highly composite odd number, having 12 divisors. It is a Harshad number, as it is divisible by the sum of its digits. It is a Zuckerman number, as it is divisible by the product of its digits. 316 316 = 22 × 79, a centered triangular number and a centered heptagonal number. 317 317 is a prime number, Eisenstein prime with no imaginary part, Chen prime, one of the rare primes to be both right and left-truncatable, and a strictly non-palindromic number. 317 is the exponent (and number of ones) in the fourth base-10 repunit prime. 318 319 319 = 11 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
311 (number)
311 (three hundred ndeleven) is the natural number following 310 and preceding 312. 311 is the 64th prime; a twin prime with 313; an irregular prime; an emirp, an Eisenstein prime with no imaginary part and real part of the form 3n - 1; a Gaussian prime with no imaginary part and real part of the form 4n - 1; and a permutable prime with 113 and 131. It can be expressed as a sum of consecutive primes in four different ways: as a sum of three consecutive primes (101 + 103 + 107), as a sum of five consecutive primes (53 + 59 + 61 + 67 + 71), as a sum of seven consecutive primes (31 + 37 + 41 + 43 + 47 + 53 + 59), and as a sum of eleven consecutive primes (11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47). 311 is a strictly non-palindromic number, as it is not palindromic in any base between base 2 and base 309. 311 is the smallest positive integer ''d'' such that the imaginary quadratic field In algebraic number theory, a quadratic field is an algebraic number fie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
307 (number)
307 is the natural number following 306 and preceding 308. In mathematics *307 is the 63rd prime number and an odd prime number. It is an isolated (i.e., not twin) prime, but because 309 is a semiprime, 307 is a Chen prime. *307 is the number of one-sided noniamonds meaning that it is the number of ways to organize 9 triangles with each one touching at least one other on the edge. *307 is the third non-palindromic number to have a palindromic square. 3072=94249. *307 is the number of solid partition Solid is a state of matter where molecules are closely packed and can not slide past each other. Solids resist compression, expansion, or external forces that would alter its shape, with the degree to which they are resisted dependent upon the ...s of 7. *307 is one of only 16 natural numbers for which the imaginary quadratic field \mathbb(\sqrt) has class number 3. References {{Integers, 3 Integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
269 (number)
269 (two hundred ndsixty-nine) is the natural number between 268 and 270. It is also a prime number. In mathematics 269 is a twin prime, and a Ramanujan prime. It is the largest prime factor of 9! + 1 = 362881, and the smallest natural number that cannot be represented as the determinant In mathematics, the determinant is a Scalar (mathematics), scalar-valued function (mathematics), function of the entries of a square matrix. The determinant of a matrix is commonly denoted , , or . Its value characterizes some properties of the ... of a 10 × 10 (0,1)-matrix. In other fields * Calf 269 was a calf that rose to fame after being rescued by Israeli activists in 2012. As a result, numerous people branded the number "269" into their bodies over 2012 and 2013. References See also * 269 AD * 269 BC * Integers {{Num-stub ... [...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] |
251 (number)
251 (two hundred ndfifty-one) is the natural number between 250 and 252. It is also a prime number. In mathematics 251 is: *a Sophie Germain prime. *the sum of three consecutive primes (79 + 83 + 89) and seven consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47). *a Chen prime. *an Eisenstein prime with no imaginary part. *a de Polignac number, meaning that it is odd and cannot be formed by adding a power of two to a prime number. *the smallest number that can be formed in more than one way by summing three positive cubes:251 = 2^3 + 3^3 + 6^3 = 1^3 + 5^3 + 5^3. Every 5 × 5 matrix Matrix (: matrices or matrixes) or MATRIX may refer to: Science and mathematics * Matrix (mathematics), a rectangular array of numbers, symbols or expressions * Matrix (logic), part of a formula in prenex normal form * Matrix (biology), the m ... has exactly 251 square submatrices. References Integers {{Num-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
227 (number)
227 (two hundred ndtwenty-seven) is the natural number following 226 and preceding 228. It is also a prime number. In mathematics 227 is a twin prime A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair or In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin prime' ..., and the start of a prime triplet. 227 is a safe prime, a regular prime, a Pillai prime, a Stern prime, and a Ramanujan prime. References Integers {{Num-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
