Fortran 中的 Prime 生成器

Question

我只是想稍微熟悉一下 Fortran（因为我可以），所以我编写了这个使用 Eratosthenes 筛生成素数的小程序。这是程序：

program prime
implicit none
integer num_primes, at, found, i
logical is_prime
integer, allocatable, dimension(:) :: primes ! array that will hold the primes
print *, "How many primes would you like to find?"
read (*, *) num_primes
allocate (primes(num_primes))
primes(1) = 2
at = 2
found = 1
do
    is_prime = .true. ! assume prime
    do i = 1, found
        if (modulo(at, primes(i)) == 0) then ! if divisible by any other element
            is_prime = .false.               ! in the array, then not prime.
            at = at + 1
            continue
        end if
    end do
    found = found + 1
    primes(found) = at
    print *, at
    at = at + 1
    if (found == num_primes) then ! stop when all primes are found
        exit
    endif
end do

结束程序主要

运行此程序将显示错误是什么，例如，尝试找到 10 个素数将产生以下数字：3、5、7、11、13、16、17、19、23。显然 16 不是素数。有什么问题？

Answer 1

这不是埃拉托色尼的筛子，它不需要modulo。 这是一种试除法，但是当你找到一个除数时，你将at 增加 1 并从你应该重新开始的下一个素数开始测试。 当您发现 15 可以被 3 整除时，at 会增加到 16，并针对 5、7、11 进行测试，这些当然不是 16 的除数，因此会打印 16。

我不是 FORTRAN 程序员，但我认为你应该替换这些行

at = at + 1
continue

通过

exit

并执行行

found = found + 1
primes(found) = at
print *, at

仅当 is_prime 为真时。

Answer 2

这是执行 Henrik 建议的工作程序（然后我做了一些格式更改）：

program prime
implicit none

integer :: num_primes, at, found, i
logical :: is_prime
integer, allocatable, dimension(:) :: primes ! array that will hold the primes

print *, "How many primes would you like to find?"
read(*, *) num_primes
allocate(primes(num_primes))
primes(1) = 2
at = 2
found = 1
do
    is_prime = .true. ! assume prime
    do i = 1, found
        if (modulo(at, primes(i)) == 0) then ! if divisible by any other element
            is_prime = .false.               ! in the array, then not prime.
            exit
        end if
    end do
    if (is_prime) then
        found = found + 1
        primes(found) = at
        print *, at
    end if
    at = at + 1
    if (found == num_primes) then ! stop when all primes are found
        exit
    end if
end do
end program prime

当你运行它时，你会得到：

 How many primes would you like to find?
20
           3
           5
           7
          11
          13
          17
          19
          23
          29
          31
          37
          41
          43
          47
          53
          59
          61
          67
          71

primes 数组将包含所有素数。这是你想要的吗？