Question

In number theory, he introduced a scheme whose pseudocode is as below. Convert this to Python and explain (line by line) what each line of your code does. Run it for different n up to n-1000. Input: an integer n > 1 . Let A be an array of Boolean values, indexed by integers 2 to n initially all set to true for i = 2, 3, 4, , not exceeding vn: if Alil is true for j-i *2,i* *2+i, i2+2i, i2+3inot exceeding n: AUl false. Output li such that Ali] is true.

Answer 1

ANSWER:

What the code does:
Finds the prime numbers below the given number n.

Python Code:

import math

def scheme(n):

A = [] #empty array

#add n elements, initially all are True

for i in range(n+1):

A.append(True)

#Now iterate from 2 to sqrt(n)

for i in range(2, int(math.sqrt(n))+1):

#if A[i] is True

if A[i] is True:

#change the values to False at positions from i*i to n, incrementing by i

#so all factors of i from i*i are set to False

for j in range(i**2, n+1, i):

A[j] = False

#Now list contains the True values only for prime numbers which don't have factors

#A[2:] is the list from index 2 to end

return A[2:]

#Test Case 1

A = scheme(100) #call function with 100

print("Primes from 2-100")

#print indices from 2 which are True

for i in range(len(A)):

if A[i] == True:

print(i+2, end=' ') #indexing from 2

print()

#Test Case 2

A = scheme(1000) #call function with 100

print("Primes from 2-1000")

#print indices from 2 which are True

for i in range(len(A)):

if A[i] == True:

print(i+2, end=' ') #indexing from 2

print()

OUTPUT:

Primes from 2-100 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 Primes from 2-1000 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 189 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 489 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997