The first 5 perfect numbers are 6, 28, 496, 8128, and 33550336.
- Perfect Number - LeetCode. only 5 perfect numbers between 1 and 100,000,000. 6, 28, 496, 8128, 33550336, these five numbers are perfect number.
Wagstaff prime numbers less than one million are 3,11,43,683,2731,43691,174763.
Around 100 c.e., Nicomachus noted that perfect numbers strike a harmony between the extremes of excess and deficiency (as when the sum of a number's divisors is too large or small), and fall in the “suitable” order: 6, 28, 496, and 8128 are the only perfect numbers in the intervals between 1, 10, 100, 1000, 10000, and ...
The first 5 perfect numbers are 6, 28, 496, 8128, and 33550336.
Now, the sum of divisors of a number, excluding the number itself, is called its aliquot sum, so we can define a perfect number as one that is equal to its aliquot sum. Hence, the sum of these factors is equal to the given number. So, 496 is a perfect number.
At the moment the largest known Mersenne prime is 2 82 589 933 − 1 2^{82 589 933} - 1 282 589 933−1 (which is also the largest known prime) and the corresponding largest known perfect number is 2 82 589 932 ( 2 82 589 933 − 1 ) 2^{82 589 932} (2^{82 589 933} - 1) 282 589 932(282 589 933−1).
It is not known whether there are any odd perfect numbers, nor whether infinitely many perfect numbers exist. The first few perfect numbers are 6, 28, 496 and 8128 (sequence A000396 in the OEIS).
The first few superperfect numbers are : 2, 4, 16, 64, 4096, 65536, 262144, 1073741824, ... (sequence A019279 in the OEIS). To illustrate: it can be seen that 16 is a superperfect number as σ(16) = 1 + 2 + 4 + 8 + 16 = 31, and σ(31) = 1 + 31 = 32, thus σ(σ(16)) = 32 = 2 × 16.
The first few unique primes are 3, 11, 37, 101, 9091, 9901, 333667, ... (OEIS A040017), which have periods 1, 2, 3, 4, 10, 12, 9, 14, 24, ... (OEIS A051627), respectively.
For example, entering either 1,000,000,000,000 or 1.0e12 will tell you ' The 1,000,000,000,000th prime is 29,996,224,275,833.
The largest known prime number (as of June 2023) is 282,589,933 − 1, a number which has 24,862,048 digits when written in base 10. It was found via a computer volunteered by Patrick Laroche of the Great Internet Mersenne Prime Search (GIMPS) in 2018.
A thousand trillions is a quadrillion: 1,000,000,000,000,000. A thousand quadrillions is a quintillion: 1,000,000,000,000,000,000.
Some numbers come after googolplex, and we have named them too. Skewes' number is one of the larger numbers than even a googolplex. This number was developed by mathematician Stanley Skewes and named after him. Skewes had a particular interest in prime numbers.
After a billion, of course, is trillion. Then comes quadrillion, quintrillion, sextillion, septillion, octillion, nonillion, and decillion.
Solution: The proper factors of 28 are 1, 2, 4, 7, and 14. The sum of these proper factors is 28. According to the definition of perfect numbers, 28 is a perfect number.
A perfect number is a rare number. To date, only 51 of them have been discovered. There are only three perfect numbers less than 1000: 6, 28, and 496.
The first 5 perfect numbers are 6, 28, 496, 8128, and 33550336.
2305843008139952128 is a perfect number.
Answer and Explanation: The number 33,550,336 is a perfect number. When you add together its factors that are less than 33,550,336, the resulting sum is equal to 33,550,336.
Now infinity is not a number but is rather a concept. One might argue can't define more numbers greater than Googolplex in any way. The answer to this is yes we can, and Graham's Number is one such number. It is exponentially bigger than Googolpex.
Here 256 is a perfect square number as it is obtained by multiplying 16 with 16. 256 can also be obtained by multiplying -16 with itself.
The smallest pair of amicable numbers is (220, 284). They are amicable because the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, of which the sum is 284; and the proper divisors of 284 are 1, 2, 4, 71 and 142, of which the sum is 220.
144 is also a perfect square because it gotten from 12×12. 169 is a perfect square because it is obtained by multiplying 13 by itself that is 13X13. Though a perfect square, 169 just like other perfect squares does not have the features that are found in 144.