5101

5101 is a prime number.

5099 and 5101 form a twin prime pair.

5101 is the initial prime in a set of four consecutive primes with common difference 6 (A033451).

5101 is a prime formed from merging four successive digits in the decimal expansion of e (A104845).

5101 is a prime whose sum of digits is 7 (A062337).

5101 is a centered 17-gonal number (A069130).

5101 has a representation as a sum of two squares: 5101 = 50² + 51². 5101 is a prime that is the sum of at least two consecutive squares (A163251).

5101 is the hypotenuse of a primitive Pythagorean triple: 5101² = 101² + 5100².

5101 divides 46²⁰ - 1.

Source: OEIS

3001

3001 is a prime number.

2999 and 3001 form a twin prime pair.

3001 is a prime whose digit sum is 4 (A062339). It is the largest 4-digit prime with minimum digit sum (A069664).

3001 is a centered decagonal number (A062786).

3001 is a prime that can be expressed as the sum of distinct powers of 3 (A077717).

3001 is 1/24 of the 24th Fibonacci number.

3001 has a representation as a sum of two squares: 3001 = 20² + 51².

3001 is the hypotenuse of a primitive Pythagorean triple: 3001² = 2040² + 2201².

3001 divides 20¹⁵ - 1.

Arthur C. Clarke wrote a book titled 3001: The Final Odyssey.

Source: Prime Curios!

1669

1669 is a prime number.

1667 and 1669 form a twin prime pair.

1669 is the smallest prime that appears in the same position as its own value when the Roman numerals (from 1 to 3999) are placed in lexicographic order. The other primes with this property are 3623 and 3631.

1669 is the smallest number whose 9th power has 29 digits.

1669² = 2785561, and 278 * (5/5) * 6 + 1 = 1669.

1669 has a representation as the sum of two squares: 1669 = 15² + 38².

1669 is the hypotenuse of a primitive Pythagorean triple: 1669² = 1140² + 1219².

Source: Prime Curios!

9931

9931 is a prime number.

9929 and 9931 form a twin prime pair. 9931 is the larger of the greatest twin prime pair with four digits (A114429).

9931 and its reversal, 1399, are both primes (A101782).

9931 is a prime with 10 as the smallest positive primitive root (A061323).

9931 is a prime p such that p - 2 and p³ - 2 are also prime (A240124).

9931 is a prime that is the sum of 8 but no fewer squared primes (A183216).

Source: OEIS

6661

6661 is a prime number.

6659 and 6661 form a twin prime pair.

6661 is the smallest beastly (containing the string 666) prime number.

6661 and its inversion, 1999, are both primes.

6661 uses only the digits 0, 1, and 5 in bases 6 (50501) and 8 (15005).

6661 has a representation as a sum of two squares: 6661 = 10² + 81².

6661 is the hypotenuse of a primitive Pythagorean triple: 6661² = 1620² + 6461².

Source: Number Gossip

1933

1933 is a prime number.

1931 and 1933 form a twin prime pair.

1933 is centered heptagonal number (A069099).

1933 = (1⁹ + 2⁸ + 3⁷ + 4⁶ + 5⁵)/5.

1933 has a representation as the sum of two squares: 1933 = 13² + 42².

1933 is the hypotenuse of a primitive Pythagorean triple: 1933² = 1092² + 1595².

1933 divides 10²¹ - 1.

Source: Prime Curios!

8839

8839 is a prime number.

8837 and 8839 form a twin prime pair.

8839 is a prime whose sum of digits is the perfect number 28 (A048517).

8839 is a prime using only the digits 0, 3, 6, 8, and 9 (A079652).

8839 is a prime that is the arithmetic mean of four successive primes (A126096).

8839 is a prime that can be expressed as a sum of distinct powers of 3 (A077717).

8839 is a number that cannot be written as a sum of three squares.

Source: OEIS

3917

3917 is a prime number.

3917 and 3919 form a twin prime pair.

3917 has a representation as a sum of two squares: 3917 = 14² + 61².

3917 is the hypotenuse of a primitive Pythagorean triple: 3917² = 1708² + 3525².

3917 divides 66¹¹ - 1.

Source: Prime Curios!

9767

9767 is a prime number.

9767 is the largest four-digit prime formed by the concatenation of two two-digit primes.

9767 and 9769 form a twin prime pair.

9767 is 14352 in base 9 (using each of the digits from 1 to 5 once).

9767 is the upper prime of a difference of 18 between consecutive primes (A031937).

9767 cannot be written as a sum of three squares.

Source: Number Gossip

1997

1997 is a prime number.

1997 and 1999 form a twin prime pair.

The 1997 substrings 199 and 997 are also primes (A069489).

1997 remains a prime when a single digit 9 is inserted between any two consecutive digits or as the leading or trailing digit (A215421).

1997 is a prime factor of 87654321.

1997 has a representation as a sum of two squares: 1997 = 29² + 34².

1997 is the hypotenuse of a primitive Pythagorean triple: 1997² = 315² + 1972².

Source: What's Special About This Number?

5503

5503 is a prime number.

5501 and 5503 form a twin prime pair.

5503 is 1111333 in base 4 (A045132).

5503 is a prime whose base 7 representation (22021) also is the base 3 representation of a prime (223) (A235470).

5503 is a member of the Fibonacci-like sequence beginning with 1 and 23 (A022393).

The cube of 5503 contains each of the digits from 1 to 9 but not 0 (A124628): 5503³ = 166,647,398,527.

Source: OEIS

2113

2113 is a prime number.

2111 and 2113 form a twin prime pair.

2113 = 1⁵ + 2⁵ + 2⁵ + 4⁵ + 4⁵ = (2⁵)² + (2⁵ + 1)².

2113 is the largest prime factor of 2²² + 1.

2113 is 100001000001 in base 2 (binary).

2113 has a representation as a sum of two squares: 2113 = 32² + 33². It is the sum of two consecutive squares.

2113 is the hypotenuse of a primitive Pythagorean triple: 2113² = 65² + 2112².

2113 divides 65⁴ - 1.

Source: Prime Curios!

3583

3583 is a prime number.

3581 and 3583 form a twin prime pair.

3583 is the smallest number requiring an addition chain of length 16 (A003064).

3583 is the sum of 11 distinct powers of 2 (A038462): 3583 = 2¹¹ + 2¹⁰ + 2⁸ + 2⁷ + 2⁶ + 2⁵ + 2⁴ + 2³ + 2² + 2¹ + 2⁰.

3583 is the smallest prime with exactly nine consecutive ones in the longest run of ones in its binary expansion (A090593).

3583 divides 95⁹ - 1.

The Commodore VIC-20 (an early 8-bit computer from 1980) had "3853 bytes free" once started up under Commodore BASIC V2.

Source: Prime Curios!

1723

1723 is a prime number.

1721 and 1723 form a twin prime pair.

1723 is a prime with distinct digits that is also a prime when the number is reversed (A046732).

1723 is the smallest of 101 consecutive primes whose sum is prime (A226380).

1723 is a central polygonal number (A002061).

1723 is the number of distinct lines through the origin in a three-dimensional cube of side length 12 (A090025).

1723 is 2324 in base 9.

1723 divides 41³ - 1.

Source: On-Line Encyclopedia of Integer Sequences

2311

2311 is a prime number.

2309 and 2311 form a twin prime pair.

2311 is the largest member in a set of twin primes generated by the formula 30(n*(n + 5)/2) + 60 +1 and - 1, for n = 1 to 10.

2311 is the concatenation of the first three prime Ulam numbers (2, 3, 11).

2311 is a Euclid number.

2311 is 4407 in base 8 and 1407 in base 12. It is 907 in base 16 and 727 in base 18.

2311 is a divisor of 41²² - 1.

November 23 is the only date that can be read as a prime in both formats: "day-month" (2311) or "month-day" (1123).

Source: Prime Curios!

571

571 is a prime number.

569 and 571 form a twin prime pair.

571 is a centered triangular number.

571 is the index of a prime Fibonacci number.

571 is 4241 in base 5. It is 1444 in base 7.

571 is a divisor of 90¹⁰ - 1.

U-571 is a 2000 film about a World War II German submarine captured by a disguised U.S. submarine.

The USS Nautilus (SSN-571) was the world's first operational nuclear-powered submarine.

Source: Prime Curios!

827

827 is a prime number.

827 and 829 form a twin prime pair.

827 is the smallest prime formed from the concatenation of two consecutive cubes.

827 is the sum of seven consecutive primes: 827 = 103 + 107 + 109 + 113 + 127 + 131 + 137.

There are 827 Ulam numbers below 10,000.

827 is the number of asymmetric trees with 11 vertices.

827 is a divisor of 20¹⁴ - 1.

The unabridged Running Press edition of Gray's Anatomy contains 827 illustrations.

Source: Prime Curios!

421

421 is a prime number.

419 and 421 are twin primes.

421 is a centered square number.

421 is the smallest number formed by the powers of two in logical order from right to left.

421 is 111 in base 20.

421 is the sum of five consecutive prime numbers: 421 = 73 + 79 + 83 + 89 + 97.

421 has a representation as a sum of two squares: 421 = 14² + 15².

421 is the hypotenuse of a primitive Pythagorean triple: 421² = 29² + 420².

All integers ever tested in the Collatz problem eventually end in the sequence 4-2-1.

Source: Prime Curios!

463

463 is a prime number.

461 and 463 form a twin prime pair.

463 is a centered heptagonal number.

463 is the smallest multidigit prime such that both the sum of the digits and the product of the digits of its square remain square.

463 divided by 595 is an excellent approximation to the common logarithm of 6.

463 is 111001111 in base 2 (binary).

463 is a divisor of 21³ - 1.

463 meters is exactly one-fourth of an international nautical mile.

Source: Prime Curios!

823

823 is a prime number.

821 and 823 form a twin prime pair. 823 forms a prime quadruplet with 821, 827, and 829.

823 = 12345/(1 + 2 + 3 + 4 + 5).

823 is a number that does not have any digits in common with its cube (557441767).

Victor Hugo's novel Les Misérables contains a sentence of 823 words, one of the longest sentences in the French language.

Source: Prime Curios!