Solved
Posts: 1,318

# Another math puzzle

Hi,

Here is another good problem I found to help test you solver skills.  This question is curtosy of Google.  Specifically the Google Treasure Hunt 2008.  Which is available for anyone to use here: http://treasurehunt.appspot.com

Since it varys the question I will paste the version I receieved here so everyone can work on the same set problem:

## Question:

Find the smallest number that can be expressed as
the sum of 19 consecutive prime numbers,
the sum of 21 consecutive prime numbers,
the sum of 405 consecutive prime numbers,
the sum of 781 consecutive prime numbers,
and is itself a prime number.

For example, 41 is the smallest prime number that can be expressed as
the sum of 3 consecutive primes (11 + 13 + 17 = 41) and
the sum of 6 consecutive primes (2 + 3 + 5 + 7 + 11 + 13 = 41).

Accepted Solutions
Solution
‎10-12-2011 06:01 PM
Posts: 1,318

## Re: Another math puzzle

Fixed the approach with sas generated values.  It finished in about one and half minutes total, so I am happy enough with it at this point:

options fullstimer macrogen mlogic mprint spool;

proc fcmp outlib=work.func.cipher;

function isprime(num);

n=0;

j=3;

do while(j<=int(sqrt(num)) and n=0);

if mod(num,j)=0 then n+1;

j+2;

end;

if n=0 then return(1);

else return(0);

endsub;

run;

%let cmplib=%sysfunc(getoption(cmplib));

options cmplib=(work.func &cmplib);

data primes;

pnum=1;

prime=2; output;

do prime=3 to 10**7 by 2;

if isprime(prime) then

do;

output;

pnum+1;

call symput('max',prime);

end;

end;

call symput('nobs',pnum);

keep prime;

run;

%macro sumprimes(seq1,seq2,seq3,seq4,max,nobs);

%do i=1 %to 4;

data _s&&seq&i(sortedby=ptot);

obsnum=1; cnt=1; iter=1; ptot=0;

do until(obsnum+&&seq&i>&nobs or ptot>&max);

set primes point=obsnum;

ptot+prime;

if cnt=&&seq&i then

do; output; iter+1; cnt=1; obsnum=iter; ptot=0; end;

else

do; obsnum+1; cnt+1; end;

end;

stop;

keep ptot;

run;

%end;

sasfile work.primes close;

data _null_;

merge %do i=1 %to 4; _s&&seq&i(in=in&i) %end;;

by ptot;

if in1 and in2 and in3 and in4 and isprime(ptot) then put 'SOLUTION FOUND: ' ptot comma20.;

run;

%mend;

%sumprimes(19,21,405,781,&max,&nobs)

options cmplib=(&cmplib);

All Replies
Super User
Posts: 10,787

## Another math puzzle

It looks like SAS can not offer me a prime numbers generator.

Does anyone tell me how to call prime numbers generator in SAS.

The generator I make spends me lots of time to get prime numbers, So I only give the answer for 19 and 21.

```prim_sum=857
p[5]=11
p[6]=13
p[7]=17
p[8]=19
p[9]=23
p[10]=29
p[11]=31
p[12]=37
p[13]=41
p[14]=43
p[15]=47
p[16]=53
p[17]=59
p[18]=61
p[19]=67
p[20]=71
p[21]=73
p[22]=79
p[23]=83

prim_sum=953
p[4]=7
p[5]=11
p[6]=13
p[7]=17
p[8]=19
p[9]=23
p[10]=29
p[11]=31
p[12]=37
p[13]=41
p[14]=43
p[15]=47
p[16]=53
p[17]=59
p[18]=61
p[19]=67
p[20]=71
p[21]=73
p[22]=79
p[23]=83
p[24]=89

data _null_;
array p{4000} _temporary_;
do i=2 to 20000;
count=0;
do j=1 to i;
if mod(i,j)=0 then count+1;
end;
if count=2 then do;x+1;p{x}=i;end;
end;
*get 19 consecutive prim number;
do m=1 to x-18;
prim_sum=0;
do n=m to m+18;
prim_sum+p{n};
end;
if prim_sum in p then do;
put prim_sum= ;
do _n=m to m+18;
put p{_n}=;
end;
stop;
end;
end;
run;

data _null_;
array p{4000} _temporary_;
do i=2 to 20000;
count=0;
do j=1 to i;
if mod(i,j)=0 then count+1;
end;
if count=2 then do;x+1;p{x}=i;end;
end;
*get 21 consecutive prim number;
do m=1 to x-20;
prim_sum=0;
do n=m to m+20;
prim_sum+p{n};
end;
if prim_sum in p then do;
put prim_sum= ;
do _n=m to m+20;
put p{_n}=;
end;
stop;
end;
end;
run;

```

Ksharp

Frequent Contributor
Posts: 94

## Another math puzzle

I haven't done much on this one, but the below is the method I was planning to use to get a list of primes.  It's written in 9.1.3, so you might have to alter the hash functions for the newer versions.  Also I think it can be made to run a little better - I'm sure it's been proven that you can stop testing for factors when you pass sqrt(integer), although I'd need to check.

For reference, the algorithm used in the sieve of erastothenes.  Rather than dividing by all integers, you only need to divide by known primes (all non-primes have prime factors).

On my system running for 20000 integers takes a few seconds.

options compress=no;

data z;

format integer 8.;

format prime 8.;

if _n_ = 1 then do;

declare hash h(ordered:'a');

h.defineKey('prime');

h.defineData('prime');

h.defineDone();

declare hiter hi('h');

end;

do i = 2 to 20000;

integer = i;

divisor_found = 0;

rc = hi.first();

do while (rc = 0);

if mod(integer,prime) = 0 then do;

divisor_found = 1;

leave;

end;

rc = hi.next();

end;

if divisor_found = 0 then do;

putlog _all_;

prime = integer;

end;

end;

h.output(dataset:'work.primes');

run;

Super User
Posts: 10,787

## Another math puzzle

Thanks. DF

I also notice this. So recode to optimize it.

But it still looks like that I need super computer to get the 405 781 .

```data _null_;
array p{100000} _temporary_;
retain x 1;
p{1}=2;
do i=2 to 200000;
prime=1;_k=1;
do while(not missing(p{_k}));
if mod(i,p{_k})=0 then prime=0;
_k+1;
end;
if prime then do; x+1;p{x}=i;end;
end;

*get 405 consecutive prim number;
do m=1 to x-404;
prim_sum=0;
do n=m to m+404;
prim_sum+p{n};
end;
if prim_sum in p then do;
put prim_sum= ;
do _n=m to m+404;
put p{_n}=;
end;
stop;
end;
end;
run;

```

Ksharp

Super User
Posts: 10,787

## Another math puzzle

But I have gotten 100 consecutive prime number.

prim_sum=2413

p[1]=2

p[2]=3

p[3]=5

p[4]=7

p[5]=11

p[6]=13

p[7]=17

p[8]=19

p[9]=23

p[10]=29

p[11]=31

p[12]=37

p[13]=41

p[14]=43

p[15]=47

p[16]=53

p[17]=59

p[18]=61

p[19]=67

p[20]=71

p[21]=73

p[22]=79

p[23]=83

p[24]=89

p[25]=97

p[26]=101

p[27]=103

p[28]=107

p[29]=109

p[30]=113

p[31]=127

p[32]=131

p[33]=137

p[34]=139

p[35]=149

p[36]=151

p[37]=157

p[38]=163

p[39]=167

p[40]=173

p[41]=179

p[42]=181

p[43]=191

p[44]=193

p[45]=197

p[46]=199

p[47]=211

p[48]=223

p[49]=227

p[50]=229

p[51]=233

p[52]=239

p[53]=241

p[54]=251

p[55]=257

p[56]=263

p[57]=269

p[58]=271

p[59]=277

p[60]=281

p[61]=283

p[62]=293

p[63]=307

p[64]=311

p[65]=313

p[66]=317

p[67]=331

p[68]=337

p[69]=347

p[70]=349

p[71]=353

p[72]=359

p[73]=367

p[74]=373

p[75]=379

p[76]=383

p[77]=389

p[78]=397

p[79]=401

p[80]=409

p[81]=419

p[82]=421

p[83]=431

p[84]=433

p[85]=439

p[86]=443

p[87]=449

p[88]=457

p[89]=461

p[90]=463

p[91]=467

p[92]=479

p[93]=487

p[94]=491

p[95]=499

p[96]=503

p[97]=509

p[98]=521

p[99]=523

p[100]=541

NOTE: DATA st

real ti

cpu tim

Ksharp

Posts: 1,318

## Another math puzzle

So, the first trick to this puzzle is figuring out the best and most efficient way to calculate prime numbers.  I will give you simple way to generate a list of primes.

data prime;

do n=1 to 10**8;

m=n+int((n-2)/8)+int((n-4)/8);

p=m+int((m-3)/2);

a=p+abs(p-3/2)+1/2;

output;

end;

keep a;

run;

With this method I can calculate 100,000,000 prime numbers in a matter of secods...

Frequent Contributor
Posts: 94

## Another math puzzle

I don't think primes can be calculating using such a method, without checking for factors.  For example, for n=23, you get:

n=23 m=27 p=39 a=77 _ERROR_=0 _N_=1

77 is divisible by 7 and 11, and therefore is not prime.

Posts: 1,318

## Another math puzzle

I got this method from the Encyclopedia of Integer Sequences, just assumed it worked...  I will check to make sure I implemented it correctly, as 77 should not be a number the formula calculates.

Posts: 1,318

## Another math puzzle

After further reading this method is only valid for the first 15 prime numbers   The formula breaks down on the 16th iteration (a(16)=49).

Super User
Posts: 10,787

## Another math puzzle

Haha.

Finally I got 405 .

```prim_sum=541283
p[8]=19
p[9]=23
p[10]=29
p[11]=31
p[12]=37
p[13]=41
p[14]=43
p[15]=47
p[16]=53
p[17]=59
p[18]=61
p[19]=67
p[20]=71
p[21]=73
p[22]=79
p[23]=83
p[24]=89
p[25]=97
p[26]=101
p[27]=103
p[28]=107
p[29]=109
p[30]=113
p[31]=127
p[32]=131
p[33]=137
p[34]=139
p[35]=149
p[36]=151
p[37]=157
p[38]=163
p[39]=167
p[40]=173
p[41]=179
p[42]=181
p[43]=191
p[44]=193
p[45]=197
p[46]=199
p[47]=211
p[48]=223
p[49]=227
p[50]=229
p[51]=233
p[52]=239
p[53]=241
p[54]=251
p[55]=257
p[56]=263
p[57]=269
p[58]=271
p[59]=277
p[60]=281
p[61]=283
p[62]=293
p[63]=307
p[64]=311
p[65]=313
p[66]=317
p[67]=331
p[68]=337
p[69]=347
p[70]=349
p[71]=353
p[72]=359
p[73]=367
p[74]=373
p[75]=379
p[76]=383
p[77]=389
p[78]=397
p[79]=401
p[80]=409
p[81]=419
p[82]=421
p[83]=431
p[84]=433
p[85]=439
p[86]=443
p[87]=449
p[88]=457
p[89]=461
p[90]=463
p[91]=467
p[92]=479
p[93]=487
p[94]=491
p[95]=499
p[96]=503
p[97]=509
p[98]=521
p[99]=523
p[100]=541
p[101]=547
p[102]=557
p[103]=563
p[104]=569
p[105]=571
p[106]=577
p[107]=587
p[108]=593
p[109]=599
p[110]=601
p[111]=607
p[112]=613
p[113]=617
p[114]=619
p[115]=631
p[116]=641
p[117]=643
p[118]=647
p[119]=653
p[120]=659
p[121]=661
p[122]=673
p[123]=677
p[124]=683
p[125]=691
p[126]=701
p[127]=709
p[128]=719
p[129]=727
p[130]=733
p[131]=739
p[132]=743
p[133]=751
p[134]=757
p[135]=761
p[136]=769
p[137]=773
p[138]=787
p[139]=797
p[140]=809
p[141]=811
p[142]=821
p[143]=823
p[144]=827
p[145]=829
p[146]=839
p[147]=853
p[148]=857
p[149]=859
p[150]=863
p[151]=877
p[152]=881
p[153]=883
p[154]=887
p[155]=907
p[156]=911
p[157]=919
p[158]=929
p[159]=937
p[160]=941
p[161]=947
p[162]=953
p[163]=967
p[164]=971
p[165]=977
p[166]=983
p[167]=991
p[168]=997
p[169]=1009
p[170]=1013
p[171]=1019
p[172]=1021
p[173]=1031
p[174]=1033
p[175]=1039
p[176]=1049
p[177]=1051
p[178]=1061
p[179]=1063
p[180]=1069
p[181]=1087
p[182]=1091
p[183]=1093
p[184]=1097
p[185]=1103
p[186]=1109
p[187]=1117
p[188]=1123
p[189]=1129
p[190]=1151
p[191]=1153
p[192]=1163
p[193]=1171
p[194]=1181
p[195]=1187
p[196]=1193
p[197]=1201
p[198]=1213
p[199]=1217
p[200]=1223
p[201]=1229
p[202]=1231
p[203]=1237
p[204]=1249
p[205]=1259
p[206]=1277
p[207]=1279
p[208]=1283
p[209]=1289
p[210]=1291
p[211]=1297
p[212]=1301
p[213]=1303
p[214]=1307
p[215]=1319
p[216]=1321
p[217]=1327
p[218]=1361
p[219]=1367
p[220]=1373
p[221]=1381
p[222]=1399
p[223]=1409
p[224]=1423
p[225]=1427
p[226]=1429
p[227]=1433
p[228]=1439
p[229]=1447
p[230]=1451
p[231]=1453
p[232]=1459
p[233]=1471
p[234]=1481
p[235]=1483
p[236]=1487
p[237]=1489
p[238]=1493
p[239]=1499
p[240]=1511
p[241]=1523
p[242]=1531
p[243]=1543
p[244]=1549
p[245]=1553
p[246]=1559
p[247]=1567
p[248]=1571
p[249]=1579
p[250]=1583
p[251]=1597
p[252]=1601
p[253]=1607
p[254]=1609
p[255]=1613
p[256]=1619
p[257]=1621
p[258]=1627
p[259]=1637
p[260]=1657
p[261]=1663
p[262]=1667
p[263]=1669
p[264]=1693
p[265]=1697
p[266]=1699
p[267]=1709
p[268]=1721
p[269]=1723
p[270]=1733
p[271]=1741
p[272]=1747
p[273]=1753
p[274]=1759
p[275]=1777
p[276]=1783
p[277]=1787
p[278]=1789
p[279]=1801
p[280]=1811
p[281]=1823
p[282]=1831
p[283]=1847
p[284]=1861
p[285]=1867
p[286]=1871
p[287]=1873
p[288]=1877
p[289]=1879
p[290]=1889
p[291]=1901
p[292]=1907
p[293]=1913
p[294]=1931
p[295]=1933
p[296]=1949
p[297]=1951
p[298]=1973
p[299]=1979
p[300]=1987
p[301]=1993
p[302]=1997
p[303]=1999
p[304]=2003
p[305]=2011
p[306]=2017
p[307]=2027
p[308]=2029
p[309]=2039
p[310]=2053
p[311]=2063
p[312]=2069
p[313]=2081
p[314]=2083
p[315]=2087
p[316]=2089
p[317]=2099
p[318]=2111
p[319]=2113
p[320]=2129
p[321]=2131
p[322]=2137
p[323]=2141
p[324]=2143
p[325]=2153
p[326]=2161
p[327]=2179
p[328]=2203
p[329]=2207
p[330]=2213
p[331]=2221
p[332]=2237
p[333]=2239
p[334]=2243
p[335]=2251
p[336]=2267
p[337]=2269
p[338]=2273
p[339]=2281
p[340]=2287
p[341]=2293
p[342]=2297
p[343]=2309
p[344]=2311
p[345]=2333
p[346]=2339
p[347]=2341
p[348]=2347
p[349]=2351
p[350]=2357
p[351]=2371
p[352]=2377
p[353]=2381
p[354]=2383
p[355]=2389
p[356]=2393
p[357]=2399
p[358]=2411
p[359]=2417
p[360]=2423
p[361]=2437
p[362]=2441
p[363]=2447
p[364]=2459
p[365]=2467
p[366]=2473
p[367]=2477
p[368]=2503
p[369]=2521
p[370]=2531
p[371]=2539
p[372]=2543
p[373]=2549
p[374]=2551
p[375]=2557
p[376]=2579
p[377]=2591
p[378]=2593
p[379]=2609
p[380]=2617
p[381]=2621
p[382]=2633
p[383]=2647
p[384]=2657
p[385]=2659
p[386]=2663
p[387]=2671
p[388]=2677
p[389]=2683
p[390]=2687
p[391]=2689
p[392]=2693
p[393]=2699
p[394]=2707
p[395]=2711
p[396]=2713
p[397]=2719
p[398]=2729
p[399]=2731
p[400]=2741
p[401]=2749
p[402]=2753
p[403]=2767
p[404]=2777
p[405]=2789
p[406]=2791
p[407]=2797
p[408]=2801
p[409]=2803
p[410]=2819
p[411]=2833
p[412]=2837
NOTE: DATA statement used (Total process time):
real time           13:35.23
cpu time            11:59.45

data _null_;
array p{500000} _temporary_;
retain x 1;
p{1}=2;
do i=2 to 1000000;
prime=1;_k=1;
do while(not missing(p{_k}));
if mod(i,p{_k})=0 then do;prime=0;leave;end;
_k+1;
end;
if prime then do; x+1;p{x}=i;end;
end;

*get 405 consecutive prim number;
do m=1 to x-404;
prim_sum=0;
do n=m to m+404;
prim_sum+p{n};
end;
if prim_sum in p then do;
put prim_sum= ;
do _n=m to m+404;
put p{_n}=;
end;
stop;
end;
end;
run;
```

Ksharp

Super User
Posts: 10,787

## Another math puzzle

I got 781. With the combiantion of Rick Aster's prime number generator. and also thanks Art297.

```prim_sum=2174729
P[3]=5
P[4]=7
P[5]=11
P[6]=13
P[7]=17
P[8]=19
P[9]=23
P[10]=29
P[11]=31
P[12]=37
P[13]=41
P[14]=43
P[15]=47
P[16]=53
P[17]=59
P[18]=61
P[19]=67
P[20]=71
P[21]=73
P[22]=79
P[23]=83
P[24]=89
P[25]=97
P[26]=101
P[27]=103
P[28]=107
P[29]=109
P[30]=113
P[31]=127
P[32]=131
P[33]=137
P[34]=139
P[35]=149
P[36]=151
P[37]=157
P[38]=163
P[39]=167
P[40]=173
P[41]=179
P[42]=181
P[43]=191
P[44]=193
P[45]=197
P[46]=199
P[47]=211
P[48]=223
P[49]=227
P[50]=229
P[51]=233
P[52]=239
P[53]=241
P[54]=251
P[55]=257
P[56]=263
P[57]=269
P[58]=271
P[59]=277
P[60]=281
P[61]=283
P[62]=293
P[63]=307
P[64]=311
P[65]=313
P[66]=317
P[67]=331
P[68]=337
P[69]=347
P[70]=349
P[71]=353
P[72]=359
P[73]=367
P[74]=373
P[75]=379
P[76]=383
P[77]=389
P[78]=397
P[79]=401
P[80]=409
P[81]=419
P[82]=421
P[83]=431
P[84]=433
P[85]=439
P[86]=443
P[87]=449
P[88]=457
P[89]=461
P[90]=463
P[91]=467
P[92]=479
P[93]=487
P[94]=491
P[95]=499
P[96]=503
P[97]=509
P[98]=521
P[99]=523
P[100]=541
P[101]=547
P[102]=557
P[103]=563
P[104]=569
P[105]=571
P[106]=577
P[107]=587
P[108]=593
P[109]=599
P[110]=601
P[111]=607
P[112]=613
P[113]=617
P[114]=619
P[115]=631
P[116]=641
P[117]=643
P[118]=647
P[119]=653
P[120]=659
P[121]=661
P[122]=673
P[123]=677
P[124]=683
P[125]=691
P[126]=701
P[127]=709
P[128]=719
P[129]=727
P[130]=733
P[131]=739
P[132]=743
P[133]=751
P[134]=757
P[135]=761
P[136]=769
P[137]=773
P[138]=787
P[139]=797
P[140]=809
P[141]=811
P[142]=821
P[143]=823
P[144]=827
P[145]=829
P[146]=839
P[147]=853
P[148]=857
P[149]=859
P[150]=863
P[151]=877
P[152]=881
P[153]=883
P[154]=887
P[155]=907
P[156]=911
P[157]=919
P[158]=929
P[159]=937
P[160]=941
P[161]=947
P[162]=953
P[163]=967
P[164]=971
P[165]=977
P[166]=983
P[167]=991
P[168]=997
P[169]=1009
P[170]=1013
P[171]=1019
P[172]=1021
P[173]=1031
P[174]=1033
P[175]=1039
P[176]=1049
P[177]=1051
P[178]=1061
P[179]=1063
P[180]=1069
P[181]=1087
P[182]=1091
P[183]=1093
P[184]=1097
P[185]=1103
P[186]=1109
P[187]=1117
P[188]=1123
P[189]=1129
P[190]=1151
P[191]=1153
P[192]=1163
P[193]=1171
P[194]=1181
P[195]=1187
P[196]=1193
P[197]=1201
P[198]=1213
P[199]=1217
P[200]=1223
P[201]=1229
P[202]=1231
P[203]=1237
P[204]=1249
P[205]=1259
P[206]=1277
P[207]=1279
P[208]=1283
P[209]=1289
P[210]=1291
P[211]=1297
P[212]=1301
P[213]=1303
P[214]=1307
P[215]=1319
P[216]=1321
P[217]=1327
P[218]=1361
P[219]=1367
P[220]=1373
P[221]=1381
P[222]=1399
P[223]=1409
P[224]=1423
P[225]=1427
P[226]=1429
P[227]=1433
P[228]=1439
P[229]=1447
P[230]=1451
P[231]=1453
P[232]=1459
P[233]=1471
P[234]=1481
P[235]=1483
P[236]=1487
P[237]=1489
P[238]=1493
P[239]=1499
P[240]=1511
P[241]=1523
P[242]=1531
P[243]=1543
P[244]=1549
P[245]=1553
P[246]=1559
P[247]=1567
P[248]=1571
P[249]=1579
P[250]=1583
P[251]=1597
P[252]=1601
P[253]=1607
P[254]=1609
P[255]=1613
P[256]=1619
P[257]=1621
P[258]=1627
P[259]=1637
P[260]=1657
P[261]=1663
P[262]=1667
P[263]=1669
P[264]=1693
P[265]=1697
P[266]=1699
P[267]=1709
P[268]=1721
P[269]=1723
P[270]=1733
P[271]=1741
P[272]=1747
P[273]=1753
P[274]=1759
P[275]=1777
P[276]=1783
P[277]=1787
P[278]=1789
P[279]=1801
P[280]=1811
P[281]=1823
P[282]=1831
P[283]=1847
P[284]=1861
P[285]=1867
P[286]=1871
P[287]=1873
P[288]=1877
P[289]=1879
P[290]=1889
P[291]=1901
P[292]=1907
P[293]=1913
P[294]=1931
P[295]=1933
P[296]=1949
P[297]=1951
P[298]=1973
P[299]=1979
P[300]=1987
P[301]=1993
P[302]=1997
P[303]=1999
P[304]=2003
P[305]=2011
P[306]=2017
P[307]=2027
P[308]=2029
P[309]=2039
P[310]=2053
P[311]=2063
P[312]=2069
P[313]=2081
P[314]=2083
P[315]=2087
P[316]=2089
P[317]=2099
P[318]=2111
P[319]=2113
P[320]=2129
P[321]=2131
P[322]=2137
P[323]=2141
P[324]=2143
P[325]=2153
P[326]=2161
P[327]=2179
P[328]=2203
P[329]=2207
P[330]=2213
P[331]=2221
P[332]=2237
P[333]=2239
P[334]=2243
P[335]=2251
P[336]=2267
P[337]=2269
P[338]=2273
P[339]=2281
P[340]=2287
P[341]=2293
P[342]=2297
P[343]=2309
P[344]=2311
P[345]=2333
P[346]=2339
P[347]=2341
P[348]=2347
P[349]=2351
P[350]=2357
P[351]=2371
P[352]=2377
P[353]=2381
P[354]=2383
P[355]=2389
P[356]=2393
P[357]=2399
P[358]=2411
P[359]=2417
P[360]=2423
P[361]=2437
P[362]=2441
P[363]=2447
P[364]=2459
P[365]=2467
P[366]=2473
P[367]=2477
P[368]=2503
P[369]=2521
P[370]=2531
P[371]=2539
P[372]=2543
P[373]=2549
P[374]=2551
P[375]=2557
P[376]=2579
P[377]=2591
P[378]=2593
P[379]=2609
P[380]=2617
P[381]=2621
P[382]=2633
P[383]=2647
P[384]=2657
P[385]=2659
P[386]=2663
P[387]=2671
P[388]=2677
P[389]=2683
P[390]=2687
P[391]=2689
P[392]=2693
P[393]=2699
P[394]=2707
P[395]=2711
P[396]=2713
P[397]=2719
P[398]=2729
P[399]=2731
P[400]=2741
P[401]=2749
P[402]=2753
P[403]=2767
P[404]=2777
P[405]=2789
P[406]=2791
P[407]=2797
P[408]=2801
P[409]=2803
P[410]=2819
P[411]=2833
P[412]=2837
P[413]=2843
P[414]=2851
P[415]=2857
P[416]=2861
P[417]=2879
P[418]=2887
P[419]=2897
P[420]=2903
P[421]=2909
P[422]=2917
P[423]=2927
P[424]=2939
P[425]=2953
P[426]=2957
P[427]=2963
P[428]=2969
P[429]=2971
P[430]=2999
P[431]=3001
P[432]=3011
P[433]=3019
P[434]=3023
P[435]=3037
P[436]=3041
P[437]=3049
P[438]=3061
P[439]=3067
P[440]=3079
P[441]=3083
P[442]=3089
P[443]=3109
P[444]=3119
P[445]=3121
P[446]=3137
P[447]=3163
P[448]=3167
P[449]=3169
P[450]=3181
P[451]=3187
P[452]=3191
P[453]=3203
P[454]=3209
P[455]=3217
P[456]=3221
P[457]=3229
P[458]=3251
P[459]=3253
P[460]=3257
P[461]=3259
P[462]=3271
P[463]=3299
P[464]=3301
P[465]=3307
P[466]=3313
P[467]=3319
P[468]=3323
P[469]=3329
P[470]=3331
P[471]=3343
P[472]=3347
P[473]=3359
P[474]=3361
P[475]=3371
P[476]=3373
P[477]=3389
P[478]=3391
P[479]=3407
P[480]=3413
P[481]=3433
P[482]=3449
P[483]=3457
P[484]=3461
P[485]=3463
P[486]=3467
P[487]=3469
P[488]=3491
P[489]=3499
P[490]=3511
P[491]=3517
P[492]=3527
P[493]=3529
P[494]=3533
P[495]=3539
P[496]=3541
P[497]=3547
P[498]=3557
P[499]=3559
P[500]=3571
P[501]=3581
P[502]=3583
P[503]=3593
P[504]=3607
P[505]=3613
P[506]=3617
P[507]=3623
P[508]=3631
P[509]=3637
P[510]=3643
P[511]=3659
P[512]=3671
P[513]=3673
P[514]=3677
P[515]=3691
P[516]=3697
P[517]=3701
P[518]=3709
P[519]=3719
P[520]=3727
P[521]=3733
P[522]=3739
P[523]=3761
P[524]=3767
P[525]=3769
P[526]=3779
P[527]=3793
P[528]=3797
P[529]=3803
P[530]=3821
P[531]=3823
P[532]=3833
P[533]=3847
P[534]=3851
P[535]=3853
P[536]=3863
P[537]=3877
P[538]=3881
P[539]=3889
P[540]=3907
P[541]=3911
P[542]=3917
P[543]=3919
P[544]=3923
P[545]=3929
P[546]=3931
P[547]=3943
P[548]=3947
P[549]=3967
P[550]=3989
P[551]=4001
P[552]=4003
P[553]=4007
P[554]=4013
P[555]=4019
P[556]=4021
P[557]=4027
P[558]=4049
P[559]=4051
P[560]=4057
P[561]=4073
P[562]=4079
P[563]=4091
P[564]=4093
P[565]=4099
P[566]=4111
P[567]=4127
P[568]=4129
P[569]=4133
P[570]=4139
P[571]=4153
P[572]=4157
P[573]=4159
P[574]=4177
P[575]=4201
P[576]=4211
P[577]=4217
P[578]=4219
P[579]=4229
P[580]=4231
P[581]=4241
P[582]=4243
P[583]=4253
P[584]=4259
P[585]=4261
P[586]=4271
P[587]=4273
P[588]=4283
P[589]=4289
P[590]=4297
P[591]=4327
P[592]=4337
P[593]=4339
P[594]=4349
P[595]=4357
P[596]=4363
P[597]=4373
P[598]=4391
P[599]=4397
P[600]=4409
P[601]=4421
P[602]=4423
P[603]=4441
P[604]=4447
P[605]=4451
P[606]=4457
P[607]=4463
P[608]=4481
P[609]=4483
P[610]=4493
P[611]=4507
P[612]=4513
P[613]=4517
P[614]=4519
P[615]=4523
P[616]=4547
P[617]=4549
P[618]=4561
P[619]=4567
P[620]=4583
P[621]=4591
P[622]=4597
P[623]=4603
P[624]=4621
P[625]=4637
P[626]=4639
P[627]=4643
P[628]=4649
P[629]=4651
P[630]=4657
P[631]=4663
P[632]=4673
P[633]=4679
P[634]=4691
P[635]=4703
P[636]=4721
P[637]=4723
P[638]=4729
P[639]=4733
P[640]=4751
P[641]=4759
P[642]=4783
P[643]=4787
P[644]=4789
P[645]=4793
P[646]=4799
P[647]=4801
P[648]=4813
P[649]=4817
P[650]=4831
P[651]=4861
P[652]=4871
P[653]=4877
P[654]=4889
P[655]=4903
P[656]=4909
P[657]=4919
P[658]=4931
P[659]=4933
P[660]=4937
P[661]=4943
P[662]=4951
P[663]=4957
P[664]=4967
P[665]=4969
P[666]=4973
P[667]=4987
P[668]=4993
P[669]=4999
P[670]=5003
P[671]=5009
P[672]=5011
P[673]=5021
P[674]=5023
P[675]=5039
P[676]=5051
P[677]=5059
P[678]=5077
P[679]=5081
P[680]=5087
P[681]=5099
P[682]=5101
P[683]=5107
P[684]=5113
P[685]=5119
P[686]=5147
P[687]=5153
P[688]=5167
P[689]=5171
P[690]=5179
P[691]=5189
P[692]=5197
P[693]=5209
P[694]=5227
P[695]=5231
P[696]=5233
P[697]=5237
P[698]=5261
P[699]=5273
P[700]=5279
P[701]=5281
P[702]=5297
P[703]=5303
P[704]=5309
P[705]=5323
P[706]=5333
P[707]=5347
P[708]=5351
P[709]=5381
P[710]=5387
P[711]=5393
P[712]=5399
P[713]=5407
P[714]=5413
P[715]=5417
P[716]=5419
P[717]=5431
P[718]=5437
P[719]=5441
P[720]=5443
P[721]=5449
P[722]=5471
P[723]=5477
P[724]=5479
P[725]=5483
P[726]=5501
P[727]=5503
P[728]=5507
P[729]=5519
P[730]=5521
P[731]=5527
P[732]=5531
P[733]=5557
P[734]=5563
P[735]=5569
P[736]=5573
P[737]=5581
P[738]=5591
P[739]=5623
P[740]=5639
P[741]=5641
P[742]=5647
P[743]=5651
P[744]=5653
P[745]=5657
P[746]=5659
P[747]=5669
P[748]=5683
P[749]=5689
P[750]=5693
P[751]=5701
P[752]=5711
P[753]=5717
P[754]=5737
P[755]=5741
P[756]=5743
P[757]=5749
P[758]=5779
P[759]=5783
P[760]=5791
P[761]=5801
P[762]=5807
P[763]=5813
P[764]=5821
P[765]=5827
P[766]=5839
P[767]=5843
P[768]=5849
P[769]=5851
P[770]=5857
P[771]=5861
P[772]=5867
P[773]=5869
P[774]=5879
P[775]=5881
P[776]=5897
P[777]=5903
P[778]=5923
P[779]=5927
P[780]=5939
P[781]=5953
P[782]=5981
P[783]=5987
NOTE: DATA statement used (Total process time):
real time           1:09.87
cpu time            1:06.65

%LET TOTAL = 1000000; * Limits the number of prime numbers generated ;
%LET DIM = 1000000; * The size of the sieve arrays used ;
%LET TIME = 2400; * Time limit in seconds ;

DATA _NULL_;
ARRAY P{&DIM} _TEMPORARY_; * Prime numbers;
ARRAY M{&DIM} _TEMPORARY_; * Multiples of prime numbers;
TIMEOUT = DATETIME() + &TIME; * Time limit;
*FILE PRINT NOTITLES;
SQUARE = 4;

DO X = 2 TO CONSTANT('EXACTINT'); * Is X prime? ;
IF DATETIME() >= TIMEOUT THEN STOP; * Time limit reached ;
IF X = SQUARE THEN DO; * Extend sieve;
IMAX + 1;
IF IMAX >= &DIM THEN leave; * Sieve size limit reached. ;
SQUARE = M{IMAX + 1};
CONTINUE;
END;
* Find least prime factor (LPF). ;
LPF = 0;
DO I = 1 TO IMAX UNTIL (LPF);
DO WHILE (M{I} < X); * Update sieve with new multiple. ;
M{I} + P{I};
END;
IF M{I} = X THEN LPF = P{I};
END;
IF LPF THEN CONTINUE; * Composite number found. ;
*PUT X @; * Write prime number in output. ;
N + 1;
IF N >= &TOTAL THEN leave; * Output maximum reached. ;
ELSE IF N <= &DIM THEN DO; * Add prime number to sieve. ;
P{N} = X;
M{N} = X*X;
END;
END;

*get 781 consecutive prim number;
do _m=1 to &dim -780;
prim_sum=0;
do _n=_m to _m+780;
prim_sum+p{_n};
end;

if prim_sum in p then do;
put prim_sum= ;
do _n=_m to _m+780;
put p{_n}=;
end;          stop;
end;

end;
run;
```

Ksharp

Valued Guide
Posts: 2,191

## Another math puzzle

I assume a list of the first 100000+ primes can be found on internet

Super User
Posts: 10,787

## Another math puzzle

Peter.

But if want 781, then at least need to generate one million prime numbers.

Frequent Contributor
Posts: 94

## Another math puzzle

However, as the author points out it should be possible to generate these yourself faster than downloading them.  Certainly if you were writing in C++ etc. it would be.

Valued Guide
Posts: 2,191