Question

What are the prime numbers between 1 and 800

Answer 1

List of prime numbers between 1 and 800:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, and 797.

To list down the all the prime numbers ranging from 1 to 800, we will use the following equation:

From numbers 5 - 39,

`6n+1,\text{and 6n-1}`

For example:

`6n-1=6(1)-1=5`
`6n+1=6(1)+1=7`
`6n-1=6(2)-1=11`
`6n+1=6(2)+1=13`
`6n-1=6(3)-1=17`
`6n+1=6(3)+1=19`

And so on..

To find number greater than 40, we will use the following formula:

`n^2+n+41`
`n^2-n+41`

For example,

`n^2+n+41=0^2+0+41=41`
`n^2+n+41=1^2+1+41=43`
`n^2+n+41=2^2+2+41=47`
`n^2+n+41=3^2+3+41=53`

And so on.. Since 800 is a huge number, I will list down all the numbers here, however, you can go ahead and try whether you get the same answer as these.

List of prime numbers between 1 and 800:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, and 797.