Einstein's Quote

Sat, 24 Aug 2024 18:38:47 +0900

Hello!

Today, I would like to talk about a quote by Albert Einstein.

The World Doesn’t Appreciate Your Good Deeds?

` The world will never appreciate the million good things you do. But it will criticize the one wrong thing you do… But do not be discouraged. “Always rise above all laughter and criticism. Stay strong.”

Albert Einstein `

This is a quote attributed to Einstein. It sharply points out the harshness of society and the bias in people’s evaluations that we feel every day.

Still, Keep Rising

“Always rise above all laughter and criticism. Stay strong.”

This following sentence can be said to be Einstein’s answer to the harsh reality mentioned above. It teaches us the importance of not yielding to criticism or ridicule, and continuing to move forward believing in ourselves.

Applying Einstein’s Teachings in Daily Life

This quote is deeply related to our daily lives. For example, there are times when your efforts at work go unrecognized, and only trivial mistakes stand out. Also, your statements on social media might be taken out of context and criticized.

At such times, try to remember this quote by Einstein. It is important to hold on to your own beliefs rather than being swayed by the evaluations of others.

Summary

This quote by Einstein teaches us the importance of “living believing in yourself without being swayed by the evaluations of others”. Let’s have the courage to pursue the path we believe in, without yielding to criticism or ridicule.

Finally, Einstein’s words once again.

“Always rise above all laughter and criticism. Stay strong.”

I hope this quote resonates with your heart and becomes a catalyst for you to take a positive step forward.

How to Enumerate Prime Numbers Up to 1000 Using the Sieve of Eratosthenes

Sun, 09 Apr 2023 12:54:24 +0900

What is the Sieve of Eratosthenes?

The Sieve of Eratosthenes is an algorithm for finding all prime numbers up to any given limit. The algorithm is simple and can be implemented with the following steps:

Create an array of boolean values with N elements, and initialize all elements to true.
Set the 0th and 1st elements of the array to false (because 0 and 1 are not prime numbers).
If the 2nd element of the array is true, output 2 as a prime number.
Set all multiples of 2 from $2^2$ onwards in the array to false.*
If the 3rd element of the array is true, output 3 as a prime number.
Set all multiples of 3 from $3^2$ onwards in the array to false.
Repeat the same process for the 4th, 5th, …, Nth elements.

*The reason for targeting elements from the square of the number onwards to become false is because the numbers smaller than the square have already been processed (enumeration is complete).

Implementation in Rust

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fn main() {
 let n = 1000;
 let mut is_prime = vec![true; n+1];
 is_prime[0] = false;
 is_prime[1] = false;
 for i in 2..=n {
 if is_prime[i] {
 println!("{}", i);
 let mut j = i * i;
 while j <= n {
 is_prime[j] = false;
 j += i;
 }
 }
 }
}

Slightly Faster Version

Considering the following points, we implement a slightly faster version:

Instead of initializing the array with true, initialize it with false (this is faster).
Since multiples of 2 are not prime numbers, omit the process of setting the elements of multiples of 2 to false.
There is no need to loop up to n; by enumerating primes up to the square root of n, you can enumerate primes up to n.

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fn main() {
 let n = 1000;
 let mut is_prime = vec![false; n+1];
 is_prime[2] = true;
 for i in (3..=n).step_by(2) {
 is_prime[i] = true;
 }
 for i in 3..=((n as f64).sqrt() as usize) {
 if is_prime[i] {
 let mut j = i * i;
 while j <= n {
 is_prime[j] = false;
 j += i * 2;
 }
 }
 }
 for i in (2..=n).filter(|&x| is_prime[x]) {
 println!("{}", i);
 }
}

References

Sieve of Eratosthenes

Math/Crypto/Quantum on kenji.blog