Send the link below via email or IMCopy
Present to your audienceStart remote presentation
- Invited audience members will follow you as you navigate and present
- People invited to a presentation do not need a Prezi account
- This link expires 10 minutes after you close the presentation
- A maximum of 30 users can follow your presentation
- Learn more about this feature in our knowledge base article
Do you really want to delete this prezi?
Neither you, nor the coeditors you shared it with will be able to recover it again.
Make your likes visible on Facebook?
You can change this under Settings & Account at any time.
Transcript of Perfect Numbers
Our presentation is on perfect numbers.
When were Perfect Numbers discovered?
Perfect numbers were first discovered by Ancient Greek mathematicians. One of them, Nicomachus, found the up to the fourth perfect number.
Later on, up to the seventh perfect number was found.
Euclid's Work in Perfect Numbers
Euclid, a famous mathematician, discovered a formula to work out a perfect number.
The formula was (2^(P-1))(2^p−1) and the solution is always an even perfect number. It works if P is a prime number.
By Harish Kang, Joel J & Derek Zhao
Odd Perfect Numbers
At the moment, no odd perfect numbers have been found, and some mathematicians have concluded that there are none.
However people are working to try and see if there are any, as people have figured out certain complex properties that the number must have.
The Formula In Action
A perfect number is one of the following two things, which are both equivalent to each other:
"Equal to the sum of its positive divisors(when excluding itself)" and:"Equal to half the sum of its positive divisors (including itself)"
The fifth perfect number was discovered by an unknown mathematician, and the sixth and seventh had been discovered by an Italian mathematician.
More even perfect numbers.
The Fifth, Sixth, and Seventh
The perfect numbers
for p = 2: 2^1(2^2−1) = 6
for p = 3: 2^2(2^3−1) = 28
for p = 5: 2^4(2^5−1) = 496
for p = 7: 2^6(2^7−1) = 8128.
Here are some examples
of the formula being
It is not known when perfect numbers were first studied and indeed the first studies may go back to the earliest times when numbers first aroused curiosity. It is quite likely, although not certain, that the Egyptians would have come across such numbers naturally given the way their methods of calculation worked. Perfect numbers were studied by Pythagoras and his followers, more for their mystical properties than for their number theoretic properties.