The prim predicate is not accurate

[mathk]

Hi,

I have use the prim? predicate to build a list of prime number. It turn out that I have mush more "prime" than expected when I ask for all prime bellow 10^5.

[soegaard]

Replying to mathk:

I have use the prim? predicate to build a list of prime number.
It turn out that I have mush more "prime" than expected when I ask for all prime bellow 10^5.

I tried calculating the number of primes below various n, and the results matches Mathematica.
Can you post your code?

#lang scheme
(require (planet soegaard/math:1:3/math))

(define (count-primes-below n)

(let loop ([c 0]

[i 1])

(if (<= i n)

(if (prime? i)

(loop (+ c 1) (+ i 1))
(loop c (+ i 1)))

c)))

(map (lambda (n) (list n (count-primes-below n)))

(list 10 100 1000 10000 100000 1000000))

((10 4)

(100 25)
(1000 168)
(10000 1229)
(100000 9592)
(1000000 78498))

; => ((10 4)

(100 25)
(1000 168)
(10000 1229)
(100000 9592)
(1000000 78498))

; From Mathematica

In[1]:= PrimePi?[1000]
Out[1]= 168

In[3]:= PrimePi?[10000]
Out[3]= 1229

In[4]:= PrimePi?[100000]
Out[4]= 9592

In[5]:= PrimePi?[1000000]
Out[5]= 78498