Numbers in number theory

This page contains numbers appearing in number theory.

List of numbers appearing in number theory

 * 163 is the largest.
 * The, which is used for finding the largest known primes, gives 194 after two iterations.
 * 210 is the product of the single-digit s.
 * 341 is the smallest to base 2.
 * 462 is the fifth largest known squarefree number of the form 2n−1Cn.
 * 496 (four hundred ninety-six) is the third . Its divisors are 1, 2, 4, 8, 16, 31, 62, 124, 248 and 496.
 * 561 is the first.
 * 561 is an interesting number primarily for the reason that \(561^2-561^1-561^0=314,159\). The resulting number 314159 contains the first six decimal digits of.
 * 561 has 3, 11, and 17 as its prime factors, incidentally the sum of those prime factors is 31, which happens to be the first two decimal digits of pi.
 * 714 and 715 are a.
 * 777 is the 124th (in the mathematical sense).
 * 1,848 is the largest known.
 * 2,047 is the smallest composite Mersenne number with prime index, in this case, (211−1). The next Mersenne number however, which is 213−1 or 8,191, is prime.
 * It is also the smallest to base 2.
 * In the fast-growing hierarchy, it is equal to f2(8)−1 and f3(2)−1.
 * The number 5,040 is the largest known factorial number which is the predecessor of a square number: 7! = 5,040 = 5,041−1 = 712−1.
 * The number 5,041 is equal to 712. It is the largest known square number which is the successor of a factorial number.
 * 5,778 is the largest number that is both a triangle and a.
 * 8,128 (eight thousand one hundred twenty-eight) is the fourth perfect number.
 * 24,310 is the fourth largest known squarefree number of the form 2n−1Cn.
 * 92,378 is the third largest known squarefree number of the form 2n−1Cn.
 * 1,352,078 is the second largest known squarefree number of the form 2n−1Cn.
 * The triple 2 + 6,436,341 = 6,436,343 is the with the highest known quality.
 * 33,550,336 (thirty-three millions five hundred fifty thousands three hundred thirty-six) is the fifth perfect number.
 * has proven that there are infinitely many s not larger than 70,000,000.
 * It is also the prize for correctly answering all sixteen questions in the Indian game show  in s.
 * 5,425,069,447 and 5,425,069,448 are the smallest pair of consecutive s.
 * 8,589,869,056 is the sixth perfect number. Furthermore, it is the largest known perfect number.
 * 262,537,412,640,768,744 is an integer equal to 640,3203 + 744. It is almost equal to the Ramanujan constant.
 * Its prime factorization is 23 × 3 × 10,939,058,860,032,031.
 * 221,256,270,138,418,389,602 is the largest known of the form 2n−1Cn.
 * It is also equal to 72!/36!2/2.
 * Its prime factorization is: 2 · 7 · 13 · 19 · 23 · 37 · 41 · 43 · 47 · 53 · 59 · 61 · 67 · 71, where · denotes multiplication.

Figurate number collisions
This list contains numbers which are two types of s at the same time.


 * 36 is the 8th and the 6th.
 * 120 is the eighth and the 15th triangular number.
 * 210 is the largest number that is both a triangle and a.
 * 1,540 is the second largest number that is both a triangle and a tetrahedral number.
 * 3,003 is the only known number larger than 1 which appears more than six times in Pascal's triangle.
 * 4,900 is the largest number that is both a square and a.
 * 7,140 is the largest number that is both a triangle and a tetrahedral number.
 * It is also the area of a in s.
 * 11,628 is the largest number that is both a triangle and a 5-simplex number.
 * 19,600 is the largest number that is both a square and a tetrahedral number.
 * 24,310 is the largest number that is both a triangle and an 8-simplex number.
 * 208,335 is the largest number that is both a triangle and a pyramid number.
 * 9,653,449 is the largest number that is both a square and a.

Waring's problem-related numbers
This list contains numbers related to.


 * 138 is the number of known nonnegative integers which cannot be written as a sum of six nonnegative cubes; the largest of which is 8,042.
 * 223 is the only nonnegative integer which cannot be written as a sum of 36 nonnegative fifth powers.
 * It is also the largest integer which cannot be written as a sum of 32, 33, 34 or 35 nonnegative fifth powers; there are only fifteen, ten, six and three nonnegative integers with this property, respectively.
 * In some countries, such as China, the Band III ends at 223 MHz.
 * It is also the number of non-control 8-bit characters.
 * 239 is the largest integer which cannot be written as a sum of eight nonnegative cubes; the only other nonnegative integer with this property is 23.
 * It is also one of only seven nonnegative integers which cannot be written as a sum of eighteen fourth powers; the largest integer with this property is 559.
 * 241 is the number of known nonnegative integers which cannot be written as a ; the largest of which is 343,867.
 * 454 is the largest integer which cannot be written as a sum of seven nonnegative cubes; there are only 17 nonnegative integers with this property.
 * It is also approximately the number of s in a.
 * Furthermore, it is (not considering myriad, lakh and -illiard) the number of numbers with an accepted English name.
 * 466 is the largest integer which cannot be written as a sum of 28, 29, 30 or 31 nonnegative fifth powers; there are only 52, 41, 31 and 22 nonnegative integers with this property, respectively.
 * 559 is the largest integer which cannot be written as a sum of eighteen fourth powers; there are only seven nonnegative integers with this property.
 * 952 is the largest integer which cannot be written as a sum of 27 nonnegative fifth powers; there are only 66 nonnegative integers with this property.
 * 1,248 is the largest integer which cannot be written as a sum of seventeen fourth powers; there are only 31 nonnegative integers with this property.
 * 4,060 is the number of known nonnegative integers which cannot be written as a sum of five nonnegative cubes; the largest of which is 1,290,740.
 * 8,042 is the largest known integer which cannot be written as a sum of six nonnegative cubes; there are only 138 known nonnegative integers with this property.
 * 13,792 is the largest integer which cannot be written as a sum of sixteen fourth powers; there are only 96 nonnegative integers with this property.
 * 343,867 is the largest known integer which cannot be written as a sum of four tetrahedral numbers; there are only 241 known nonnegative integers with this property.
 * 1,290,740 is the largest known integer which cannot be written as a sum of five nonnegative cubes; there are only 4,060 known nonnegative integers with this property.
 * 113,936,676 is the number of known nonnegative integers which cannot be written as a sum of four nonnegative cubes; the largest of which is 7,373,170,279,850.
 * Its factorization is 22 · 3 · 7 · 1,356,389.
 * 7,373,170,279,850 is the largest known integer which cannot be written as a sum of four nonnegative cubes; there are only 113,936,676 known nonnegative integers with this property.
 * Its prime factorization is 2 × 52 × 18,521 × 7,961,957.

Approximations of these numbers
For 8,042:

For 221,256,270,138,418,389,602: