Seventy one (71)
1. It is a 20th Prime number which makes a twin prime with the next prime 73.
2. It is a Chen Prime. A prime number p is called a Chen prime if p + 2 is either a prime or a product of two primes. It is named after Chen Jingrun. There are infinitely Chen primes and the first ten are- 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.
3. It is also a Pillai prime named after the Indian mathematician Subbayya Sivasankaranarayana Pillai. A Pillai prime is a prime number p for which there is no integer n > 0 such that the factorial of n is one less than a multiple of the prime, but the prime is not one more than a multiple of n. The first 10 Pillai primes are 23, 29, 59, 61, 67, 71, 79, 83, 109 and 137. Mathematically
4. It is a 5th centered heptagonal number. A centered heptagonal number is a centered figurative number that represents a heptagon with a dot in the centre and other dot surrounding in heptagonal layers. It is genereated by using the formula
5. The cube of 71 contains all odd numbers from 3 to 11.
71^3 = 357911
6. The cube of 71 is the only two digit cube that ends with 11
7. The atomic number of Lanthanide is 71.
8. It is one of the number in the last pair of Brocard number. Pairs of numbers (n ,m) that solves the Brocard’s problem which states to find the integral value of n for which this was posed by Henri Brocard in 1876 and later solved by Srinivasa Ramanujan independently in 1913 without knowing that this problem had been solved earlier. There are only three pairs of such number- (4, 5), (5, 11) and (7, 11).
9. Sum of all previous prime numbers is divisible by 71.
2 + 3 + 5 + 7 + 11+ --- + 67 is divisible by 71.
10. The square of 71 can be expressed the sum of digits of its factorial.
71^2 = 7! + 1!
DR RAJESH KUMAR THAKUR
rkthakur1974@gmail.com
1. It is a 20th Prime number which makes a twin prime with the next prime 73.
2. It is a Chen Prime. A prime number p is called a Chen prime if p + 2 is either a prime or a product of two primes. It is named after Chen Jingrun. There are infinitely Chen primes and the first ten are- 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.
3. It is also a Pillai prime named after the Indian mathematician Subbayya Sivasankaranarayana Pillai. A Pillai prime is a prime number p for which there is no integer n > 0 such that the factorial of n is one less than a multiple of the prime, but the prime is not one more than a multiple of n. The first 10 Pillai primes are 23, 29, 59, 61, 67, 71, 79, 83, 109 and 137. Mathematically
4. It is a 5th centered heptagonal number. A centered heptagonal number is a centered figurative number that represents a heptagon with a dot in the centre and other dot surrounding in heptagonal layers. It is genereated by using the formula
5. The cube of 71 contains all odd numbers from 3 to 11.
71^3 = 357911
6. The cube of 71 is the only two digit cube that ends with 11
7. The atomic number of Lanthanide is 71.
8. It is one of the number in the last pair of Brocard number. Pairs of numbers (n ,m) that solves the Brocard’s problem which states to find the integral value of n for which this was posed by Henri Brocard in 1876 and later solved by Srinivasa Ramanujan independently in 1913 without knowing that this problem had been solved earlier. There are only three pairs of such number- (4, 5), (5, 11) and (7, 11).
9. Sum of all previous prime numbers is divisible by 71.
2 + 3 + 5 + 7 + 11+ --- + 67 is divisible by 71.
10. The square of 71 can be expressed the sum of digits of its factorial.
71^2 = 7! + 1!
DR RAJESH KUMAR THAKUR
rkthakur1974@gmail.com
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