47 is a prime number from 1-100. 47 has 2 factors, 1 and 47. It's the fifteenth prime number, the fifteenth prime number from 1-100 and also the second Carol prime. The primorial of 47 is 614,889,782,588,491,410.
Proofs[]
— 47 is divisible by 1.
— 47 is not divisible by 2-46.
— 47 is divisible by 47.
Therefore, 47 has 2 factors and is prime.
As an Exponent of Mersenne Number[]
247 - 1, which is the number 140,737,488,355,327, is divisible by 2,351, 4,513, and 13,264,529, and is therefore not a prime number.
Relationship with other odd numbers[]
The numbers before[]
- 41 is the second previous prime number.
- The difference between 47 and 41 is 6. Therefore, they are sexy primes.
- 43 is the previous prime number.
- The difference between 47 and 43 is 4. Therefore, they are cousin primes.
- The previous odd number, 45, is a composite number. It can be factored into 32 x 5.
The numbers after[]
- The next odd number, 49, is a composite number. It is a square number, equal to 72.
- 51 is a composite number. It can be factored into 3 x 17.
- 53 is the next prime number.
- The difference between 53 and 47 is 6. Therefore, they are sexy primes.
Usage[]
Science[]
- 47 is the atomic number of silver.
Astronomy[]
- The ancient Mesopotamians discovered the 47-year cycle of Mars, where every 47 years, Mars returns to the same position among the stars and is in the same relationship to the Earth and the Sun.
Trivia[]
- 47 is The last Prime Number that comes before the first Untouchable Composite number 52.
- 47 is also the largest space between untouchable numbers (5 and 52), and it is one of two odd spaces between untouchable numbers, the second such space being the number 3 between the first untouchable numbers (2 and 5), this is because 5 is the only odd untouchable number. Moreover, the first composite untouchable number 52 is the sum of two prime numbers 47 and 5 (i.e. the previous untouchable number, and at the same time the last prime untouchable and the only odd one). Interestingly, all untouchable numbers except the first two primes 2 and 5 are composite and even, the next such numbers are 52, 88, 96, 120 etc.
Just a little curiosity about untouchable numbers, why the density increases so much. This happens because as the numbers get larger, the density of prime numbers decreases. As we know, untouchable numbers cannot express the sum of the divisors of any number, and numbers 1 greater than the prime number express the square of the prime number, and numbers 3 greater than the prime number express twice the prime number.
- eg. 2^2=4, factors of 4, (1+2=3), so 3 cannot be a untocuhable number.
- eg. 3^2=9, factors of 9, (1+3=4), so 4 cannot be a untocuhable number.
- eg. 3*2=6, factors of 6, (1+2+3=6), so 6 cannot be a untocuhable number.
- eg. 5^2=25, factors of 25, (1+5=6), so 6 cannot be a untocuhable number.
- eg. 5*2=10, factors of 10, (1+2+5=8), so 8 cannot be a untocuhable number.
And so on. The density of prime numbers is high at the beginning, and the first untouchable number after such a long interval is 52. This is because the interval between prime numbers 47 and 53 is sufficient and is 6, while 52 is 5 greater than 47, so 52 can be the first untouchable composite number. And then untouchable numbers appear more and more often, which means that 47 is the largest gap between untouchable numbers.