Good prime
Encyclopedia
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.
A good prime satisfies the inequality
for all 1 ≤ i ≤ n−1. pn is the nth prime.
There are infinitely many good primes. The first good primes are
Prime number
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...
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.
A good prime satisfies the inequality
for all 1 ≤ i ≤ n−1. pn is the nth prime.
There are infinitely many good primes. The first good primes are
- 5, 1111 (number)11 is the natural number following 10 and preceding 12.Eleven is the first number which cannot be counted with a human's eight fingers and two thumbs additively. In English, it is the smallest positive integer requiring three syllables and the largest prime number with a single-morpheme name...
, 1717 (number)17 is the natural number following 16 and preceding 18. It is prime.In spoken English, the numbers 17 and 70 are sometimes confused because they sound similar. When carefully enunciated, they differ in which syllable is stressed: 17 vs 70...
, 2929 (number)29 is the natural number following 28 and preceding 30.-In mathematics:It is the tenth prime number, and also the fourth primorial prime. It forms a twin prime pair with thirty-one, which is also a primorial prime. Twenty-nine is also the sixth Sophie Germain prime. It is also the sum of three...
, 3737 (number)37 is the natural number following 36 and preceding 38.-In mathematics:It is a prime number, the fifth lucky prime, the first irregular prime, the third unique prime and the third cuban prime of the form...
, 4141 (number)41 is the natural number following 40 and preceding 42.-In mathematics:Forty-one is the 13th smallest prime number. The next is forty-three, with which it comprises a twin prime...
, 5353 (number)53 is the natural number following 52 and preceding 54.-In mathematics:Fifty-three is the 16th prime number. It is also an Eisenstein prime....
, 5959 (number)59 is the natural number following 58 and preceding 60.-In mathematics:Fifty-nine is the 17th smallest prime number. The next is sixty-one, with which it comprises a twin prime. 59 is an irregular prime, a safe prime and the 14th supersingular prime. It is an Eisenstein prime with no imaginary...
, 6767 (number)67 is the natural number following 66 and preceding 68. It is an odd number.-In mathematics:Sixty-seven is the 19th prime number , an irregular prime, a lucky prime, the sum of five consecutive primes , and a Heegner number.Since 18! + 1 is divisible by 67 but 67 is not one more than a multiple of...
, 7171 (number)71 is the natural number following 70 and preceding 72.-In mathematics:71 is the algebraic degree of Conway's constant, a remarkable number arising in the study of look-and-say sequences....
, 9797 (number)97 is the natural number following 96 and preceding 98.-In mathematics:97 is the 25th prime number , following 89 and preceding 101. 97 is a Proth prime as it is 3 × 25 + 1.The numbers 97, 907, 9007, 90007 and 900007 are happy primes...
, 101101 (number)101 is the natural number following 100 and preceding 102.It is variously pronounced "one hundred and one" / "a hundred and one", "one hundred one" / "a hundred one", and "one oh one"...
, 127127 (number)127 is the natural number following 126 and preceding 128.- In mathematics :*As a Mersenne prime, 127 is related to the perfect number 8128. 127 is also an exponent for the Mersenne prime 2127 - 1, making 127 a double Mersenne prime...
, 149149 (number)149 is the natural number between 148 and 150. It is also a prime number.-In mathematics:*149 is the 35th prime number, and with the next prime number, 151, is a twin prime, thus 149 is a Chen prime. 149 is a strong prime in the sense that it is more than the arithmetic mean of its two neighboring...
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