c++ Multiples of 5 in sieve of atkin implemenation - c++

Question

I'm solving a problem over at project euler which requires me to find the sum of all primes under 2 million. I tried to implement sieve of atkin and strangely it sets numbers like 65,85 as primes. I looked at the code and algorithm for over a a day but can't find anything wrong. I'm sure it must be something silly but i can't find it. Thanks in advance
i'm using visual studio express 2012.
here's the code:
#include "stdafx.h"
#include <iostream>
#include <math.h>
#include <vector>
#include <fstream>
#include <conio.h>
int main(){
long long int limit,n;
std::cout<<"Enter a number...."<<std::endl;
std::cin>>limit;
std::vector<bool> prime;
for(long long int k=0;k<limit;k++){ //sets all entries in the vector 'prime' to false
prime.push_back(false);
}
long long int root_limit= ceil(sqrt(limit));
//sive of atkin implementation
for(long long int x=1;x<=root_limit;x++){
for(long long int y=1;y<=root_limit;y++){
n=(4*x*x)+(y*y);
if(n<=limit && (n%12==1 || n%12==5)){
prime[n]=true;
}
n=(3*x*x)+(y*y);
if(n<=limit && n%12==7){
prime[n]=true;
}
n=(3*x*x)-(y*y);
if(x>y && n<=limit && n%12==11){
prime[n]=true;
}
}
}
//loop to eliminate squares of the primes(making them square free)
for(long long int i=5;i<=root_limit;i++){
if(prime[i]==true){
for(long long int j=i*i;j<limit;j+=(i*i)){
prime[j]=false;
}
}
}
unsigned long long int sum=0;
//print values to a seperate text file
std::ofstream outputfile("data.txt");
outputfile<<"2"<<std::endl;
outputfile<<"3"<<std::endl;
for(long long int l=5;l<limit;l++){
if(prime[l]==true){
sum+=l;
outputfile<<l<<std::endl;;
}
}
outputfile.close();
std::cout<<"The sum is...."<<sum+5<<std::endl;
prime.clear();
return 0;
}
and hers the data.txt i pointed out few errors
2
3
5
7
11
13
17
19
23
29
31
37
41
43
47
53
59
61
65<-----
67
71
73
79
83
85<-----
89
91
97
101
103
107
109
113
127
131
137
139
143
145<----
149
151
157
163
167
173
179
181
185<----
191
193
197
199
205
211
221
223
227
229
233
239
241
247
251
257
259
263
265
269
271
277
281
283
293
299
305
307
311
313
317
331
337
347
349
353
359
365
367
373
377
379
383
389
397
401
403
407
409
419
421
427
431
433
439
443
445
449
457
461
463
467
479
481
485
487
491
493
499
503
505
509
511
521
523
533
541
545
547
557
559
563
565
569
571
577
587
593
599
601
607
611
613
617
619
629
631
641
643
647
653
659
661
671
673
677
679
683
685
689
691
697
701
703
709
719
727
733
739
743
745
751
757
761
763
767
769
773
785
787
793
797
803
809
811
821
823
827
829
839
851
853
857
859
863
865
871
877
881
883
887
901
905
907
911
919
923
929
937
941
947
949
953
965
967
971
977
983
985
991
997
1009
1013
1019
1021
1027
1031
1033
1037
1039
1049
1051
1061
1063
1067
1069
1073
1079
1087
1091
1093
1097
1099
1103
1105
1109
1117
1123
1129
1145
1147
1151
1153
1157
1159
1163
1165
1171
1181
1187
1189
1193
1199
1201
1205
1213
1217
1223
1229
1231
1237
1241
1249
1259
1261
1267
1277
1279
1283
1285
1289
1291
1297
1301
1303
1307
1313
1319
1321
1327
1339
1345
1351
1361
1367
1373
1381
1385
1387
1391
1399
1403
1405
1409
1417
1423
1427
1429
1433
1439
1447
1451
1453
1459
1465
1469
1471
1481
1483
1487
1489
1493
1499
1511
1513
1517
1523
1531
1537
1543
1549
1553
1559
1565
1567
1571
1579
1583
1585
1591
1597
1601
1603
1607
1609
1613
1619
1621
1627
1637
1649
1651
1657
1663
1667
1669
1679
1685
1687
1693
1697
1699
1703
1709
1717
1721
1723
1727
1733
1739
1741
1745
1747
1753
1759
1765
1769
1777
1781
1783
1787
1789
1801
1807
1811
1823
1831
1843
1847
1853
1861
1865
1867
1871
1873
1877
1879
1885
1889
1891
1901
1907
1913
1921
1931
1933
1937
1939
1945
1949
1951
1961
1963
1973
1979
1985
1987
1991
1993
1997
1999

Answer 1

You're supposed to flip the entries to the sieve list. In the first nested for loops instead of prime[n]=true; you should have prime[n]=!prime[n];