1559

1559 is a prime number. It is a Sophie Germain prime because 2 x 1559 + 1 = 3119 is also prime (A005384).

Reversing the digits of 1559 produces the prime 9551. 1559 is the smallest such prime that becomes a semiprime when any single digit is removed.

1559 is the smallest prime p with 16 consecutive quadratic residues mod p.

1559 is the number of different ways to divide an 11 x 11 square into sub-squares, considering only the list of parts (A034295).

1559 is 2010202 in base 3. It is 2122 in base 9.

Source: Prime Curios!

8111

8111 is a prime number. It is a Sophie Germain prime because 2 x 8111 = 16223 is also prime. Every digit of 8111 is a perfect cube (A061247 and A066592).

8111 is a prime that results from merging four successive digits in the decimal expansion of pi (A104824).

8111 is the concatenation of the first two digits and the last two digits of the 35th Mersenne prime (A138863).

8111 is 102010102 in base 3. It is 12112 in base 9 (A032930).

Source: OEIS

4391

4391 is a prime number. It is a Sophie Germain prime because 2 x 4391 + 1 = 8783 is also a prime.

4391 is the smaller of two consecutive Sophie Germain primes with the same digital sum (A118506).

4391 is the sum of the first 47 primes minus 47 (A101301).

4391 is a number that cannot be written as a sum of three squares.

4391 is 3332 in base 11 (A032811).

Source: OEIS

5303

5303 is a prime number. It is a Sophie Germain prime because 2 x 5303 + 1 = 10607 is also a prime. The sum of the digits of 5303 (11) is also a Sophie Germain prime (A118504).

5303 is a balanced prime (the average of the previous prime and the following prime) (A006562). 5297, 5303, and 5309 are three consecutive primes (A053070).

5303 is a prime that is the sum of five consecutive composite numbers (A060330).

Source: OEIS

2003

2003 is a prime number. It is a Sophie Germain prime because 2 x 2003 + 1 = 4007 is also a prime.

2003 is formed from the first two primes (2 and 3) separated by two zeroes. Add 2³, then 2 x 3 to get the next two primes: 2011 and 2017.

The concatenation of numbers from 2000 to 2003 (2000200120022003) is a prime.

2003 is the only known prime of the form 2 x 10^p + p, where p and p + 4 are primes (with p = 3).

2003 is 133103 in base 4 and 31003 in base 5.

2003 divides 22¹³ - 1.

2003 was the first prime year of the current millennium. The next two are 2011 and 2017.

Source: Number Gossip and Prime Curios!

1889

1889 is a prime number. It is a Sophie Germain prime because 2 x 1889 + 1= 3779 is also prime (A005384).

1889 is the smallest prime such that it and the next four primes (1889, 1901, 1907, 1913, and 1931) are all 5(mod 6), that is, leave a remainder of 5 when divided by 6.

1889 is the smallest prime with digit sum 26 (A067180).

1889 and 118891 are both primes (A069687).

1889 has a representation as a sum of two squares: 1889 = 17² + 40².

1889 is the hypotenuse of a primitive Pythagorean triple: 1889² = 1311² + 1360².

1889 is a divisor of 85⁸ - 1.

The Wall Street Journal was first published in the year 1889.

Source: Prime Curios!

761

761 is a prime number. It is a Sophie Germain prime because 2 x 761 + 1 = 1523 is also prime.

761 is a centered square number.

761 is the sum of all primes numbers up to 79.

761 has a representation as a sum of two squares: 761 = 19² + 20².

761 is the hypotenuse of a primitive Pythagorean triple: 761² = 39² + 760².

A sequence of six nines (known as the Feynman point) begins immediately after the 761st decimal place of pi. Physicist Richard Feynman expressed a wish to memorize the digits of pi as far as that point so that when reciting them he would be able to end with ". . . nine, nine, nine, nine, nine, nine, and so on."

Source: Prime Curios!

1733

1733 is a prime number. It is a Sophie Germain prime because 2 x 1733 + 1 = 3467 is also prime.

1733 is the smallest prime that contains exactly six smaller primes as substrings: 3, 7, 17, 73, 173, 733.

1733 is palindromic in base 3: 2101012. It is 565 in base 18.

1733 has a representation as a sum of two squares: 1733 = 17² + 38².

1733 is the hypotenuse of a primitive Pythagorean triple: 1733² = 1155² + 1292².

Source: What's Special About This Number?

491

491 is a prime number. It is a Sophie Germain prime (A005384) because 2 x 491 + 1 = 983 is also prime.

491 is a prime number with distinct, nonprime digits (A034844) in English consecutive order: four, nine, one. Each digit is also a square.

It is conjectured that 491 is the smallest prime not of the form x³ + y³ + 2z³.

491 is the smallest number n such that the largest prime factors of the numbers n through n + 4 decrease.

Source: Prime Curios!

2351

2351 is a prime number. It is a Sophie Germain prime because 2 x 2351 + 1 = 4703 is also prime.

2351²³⁵¹ ends in the digits 2351.

There are 6907 digits in 2351! Note that 6907 is prime.

2351 is in the middle of a sequence of 17 consecutive primes whose sum is also prime: 2293 + 2297 + . . . + 2351 + 2393 + 2399 = 39971 is prime and 17 is prime.

2351 is the sum of all three-digit Fibonacci numbers.

Source: Prime Curios!

719

719 is a prime number. It is a Sophie Germain prime because 2 x 719 + 1 = 1439, also a prime.

719 is a number that can be expressed as both a factorial prime (6! - 1) and as an abundant number less 1.

719 is the number of rooted trees with 12 vertices.

719 is a right-truncatable prime number: 719, 71, and 7 are all primes.

719, 197, and 971 are all primes.

The hour and second hands of an analog clock align 719 times every twelve hours.

Source: Prime Curios!

191

191 is a prime number. It is a Sophie Germain prime because 2 x 191 + 1 = 383 is also a prime. In addition, the resulting number is a palindrome.

191 and 193 form a twin prime pair.

191 is the maximum number of regions into which 19 lines divide the plane.

191 is the smallest palindromic prime whose digit sum (1 + 9 + 1 = 11) is a multidigit palindromic prime. It is also the smallest multidigit palindromic prime that yields a palindrome when multiplied by the next prime: 191 x 193 = 36863.

191 is the smallest prime in a set of four consecutive primes (191, 193, 197, 199) whose sum of digits is another set of four primes (11, 13, 17, 19).

The common U.S. coins--a silver dollar, half-dollar, quarter, dime, nickel, and penny--add up to 191 cents.

Source: Number Gossip

113

113 is a prime number. It is a Sophie Germain prime because 2 x 113 + 1 = 227 is also a prime.

113 is the smallest three-digit prime whose product and sum of digits is prime: 1 x 1 x 3 = 3 and 1 + 1 + 3 = 5.

113 has a representation as a sum of two squares: 113 = 7² + 8² (the sum of two consecutive squares).

113 is the hypotenuse of a primitive Pythagorean triple: 113² = 15² + 112².

113 is a centered square number.

113² = 12769 and its reversal 96721 = 311².

A113 is the license plate number of Andy's mom's vehicle in the film Toy Story.

Source: Number Gossip and Prime Curios!

743

743 is a prime number. It is a Sophie Germain prime because 2 x 743 + 1 = 1487 is a prime.

743 is the number of independent sets of the graph of the tesseract (four-dimensional cube).

648⁷ + 139968⁴ = 7558272³.

743 is 616 in base 11 and 212 in base 19.

The sun's mass is about 743 times the combined mass of all the planets in the solar system.

Source: Number Gossip

653

653 is a prime number. It is a Sophie Germain prime because 2 x 653 + 1 = 1307 is a prime.

653 is the first three-digit prime number to occur in the decimal expansion of pi.

653 has a representation as a sum of two squares: 653 = 13² + 22².

653 is the hypotenuse of a primitive Pythagorean triple: 653² = 315² + 572².

653 is the sum of the squares of five consecutive primes: 653 = 5² + 7² + 11² + 13² + 17².

ARINC 653 is a software specification for space and time partitioning in safety-critical avionics real-time operating systems.

Source: Number Gossip

659

659 is a prime number. It is a Sophie Germain prime because 2 x 659 + 1 = 1319 is also a prime.

0659, 2659, 3659, 5659, and 6659 are all primes.

659 and 661 form a twin prime pair.

659 is a divisor of 12⁷ - 1.

659 is the sum of seven consecutive primes: 659 = 79 + 83 + 89 + 97 + 101 + 103 + 107.

659 Nestor is a Jupiter Trojan asteroid that orbits along Jupiter's path. It was discovered in 1908.

Source: Prime Curios!

179

179 is a prime number. 179 is a Sophie Germain prime because 2 x 179 + 1 = 359, a prime.

179 and 181 form a twin prime pair.

179 = (17 x 9) + (17 + 9).

179 has a square comprised of the digits 0 to 4: 179² = 32041.

179 x 79 = 14141.

There are 179 even days in one year.

Source: Number Gossip

419

419 is a prime number.

419 is also a Sophie Germain prime because 2 x 419 + 1 = 839 is also prime. It is the 22nd Sophie Germain prime, and 22 = 2 x 11 is the product of two Sophie Germain primes.

419 and 421 form a twin prime pair.

419 is a divisor of 13¹¹ - 1.

419 is the smallest number that when divided by 2, 3, 4, 5, 6, and 7 leaves remainders of 1, 2, 3, 4, 5, and 6, respectively. Also, 419 is 1 less than the least common multiple of the first seven integers.

419, 41, and 19 are all primes. Their reversals, 914, 14, and 91, are all semiprimes.

Dutch naturalist and microscopy pioneer Anton van Leeuwenhoek (1632-1723) ground a total of 419 lenses during his life.

Source: Prime Curios!

359

359 is a prime number. It is a Sophie Germain prime because 2 x 359 + 1 = 719, a prime.

359 is a number that cannot be written as a sum of three squares.

359 = -1 + 2³ x 45.

The 359th, 360th, and 361st decimal digits of pi are 360.

359 has a base 3 representation (111022) that ends with its base 7 representation (1022), which is also true for 357 and 358.

In the Star Trek imaginary universe, the Battle of Wolf 359 was the Federation's first major battle against a group of cyborgs.

Source: Prime Curios!

173

173 is a prime number. It is a Sophie Germain prime because 2 x 173 + 1 = 347, which is also prime.

173 has a representation as a sum of two squares: 173 = 2² + 13². It is the sum of the squares of two Fibonacci numbers, 2 and 13.

173 is the hypotenuse of a primitive Pythagorean triple: 173² = 52² + 165².

173 is the only prime whose sum of cubed digits equals its reversal: 1³ + 7³ + 3³ = 371.

173 is the largest known prime whose square (29929) and cube (5177717) have no digits in common.

173 = 1 + 2² + 2³ + 2⁵ + 2⁷, where the exponents are consecutive primes.

In the 1993 movie The Sandlot, The Beast (a ferocious dog) is said to have eaten 173 guys.

Source: Prime Curios!