Question

Write a procedure stol in scheme that outputs a set of the M smallest prime numbers in increasing order. Use the algorithmic idea known as a sieve. Let S be the solution list, initially empty. Begin with the consecutive list of numbers L = 2,3,4, ... ,N where N is sufficiently large, which means at least equal to the Mth smallest prime number (unfortunately one cannot assume that the Mth smallest prime number is known when the code is run). Move the smallest number in L (that is, 2) to S. Remove all multiples of 2 from L to get L = 3,5,7,9,11, ... ,N Move the smallest number in L (now 3) to S (which is now the list [2,3]) and remove all multiples of 3 from L to get: L = 5,7,11,13,17,19,23, ... ,N Repeat to get S = [2,3,5] L = 7,11,13,17,19,23,29, ... ,N Repeat to get S = [2,3,5,7] L = 11,13,17,19,23,29,31,37,41,43,47, ... ,N and so on. The first 100 primes are: 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

Answer 1

*** Not sure what is procedure slot scheme, I'll try my best to answer this question ***

- First consider two list 'S' and 'L'.

- Consider S as solution list and L as a list of natural numbers except 1.

- Then L contains [2,3,4,5,6,.....N].

- Now lets take the first element 2 and place it in S, so now S contains [2].

- Now remove all the multiplies of 2 from list L [ that means ' if (L[i]%2==0) { remove L[i] } ' ], then repeat this procedure, like now take the next element 3 and place in S, now that list contains [2,3], and start removing multiplies of 3, and carry on like this.

- And continue this procedure till 100 such prime numbers are in list S.

** This answer is written this like since, there is no mention of any specific programming language, I hope you understand and do well, please give a thumbs up after reading this answer. Thank you so much **