How is prime density up to x defined in the video?

Conditions

• x is a positive integer search bound.
• Density is computed by dividing the prime count by the search size.

Reasoning, step by step

1. Identify the number of primes less than x.
2. Identify the search size x.
3. Divide the prime count by x to obtain the density.

Example

The video displays the fraction # PRIMES over SIZE and computes $25/100 = 25$% for the first 100 integers.

Common misconceptions

• Confusing the cumulative count of primes with their density; the count increases while density decreases.
• Assuming density is a fixed constant rather than a ratio dependent on the search size x.

Watch the explanation

Explore next

• Why does prime density decrease as x grows?
• What formula approximates prime density for large x?
• How is the Prime Number Theorem derived from prime density?