197 (number)
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197 is a natural number that falls between 196 and 198. It is a prime number, meaning it has no divisors other than 1 and itself. In base ten, it is composed of three digits (100 + 90 + 7).
In number theory, 197 has several notable properties, particularly relating to nearby prime numbers and various transformations of its digits.
Mathematical properties
197 is the sum of the first twelve prime numbers: 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 = 197. It also forms a twin prime pair with 199, since both are prime and differ by two.
197 can be expressed as the sum of two squares: 197 = 14² + 1² (196 + 1). This property occurs in primes that leave a remainder of 1 when divided by 4, in accordance with Fermat's theorem on sums of two squares.
Digit rotations
When the digits of 197 are rotated in sequence, the results—971 and 719—are both prime numbers. For this reason, 197 is classified as a circular prime, a prime number all of whose digit rotations are also prime.
Notation and other uses
In Roman numerals, 197 is written CXCVII. In binary, it is 11000101. The number 197 also appears in various general uses such as historical records, road numbers, and different coding systems; specific applications are matters of institutional or organizational convention rather than mathematical property.