20200209, 11:36  #78  
Dec 2008
you know...around...
2^{2}×5×29 Posts 
Quote:
If you can't use the program right now, that's perfectly okay. All I needed was a tiny indication of how useful my code is, so thanks for the reply 

20200209, 12:08  #79 
Feb 2003
771_{16} Posts 
Thanks for sharing your VBA code, mart_r!
I will have a look into it and give it a try when I'm back in my office next week (don't have Excel at home)... 
20200209, 22:35  #80  
May 2018
193 Posts 
Late gaps
Quote:
Last fiddled with by Bobby Jacobs on 20200209 at 22:37 

20200212, 19:21  #81 
Dec 2008
you know...around...
2^{2}·5·29 Posts 
I finally got around comparing the speed of Thomas' and my code on my only PC that's able to run both programs.
My former code was actually slower than I thought, but the current one below is almost on par, and may be faster on other systems. In the range 6e15+, its throughput is about 780e6/s on my workplace PC. Maybe going to run it for this search, after some minor other projects... Code:
'please enter your values of choice here: k1=range start, k2=range end, mg&=mingap report ' k1 = 9E+16 k2 = 9.00005E+16 mg& = 200000 ' tm = Timer Cells(1, 4) = "initializing..." Dim p&(22914109), c&(700244), d&(17506124), o&(22914109, 4), e&(22914109), a%(215656441), aa%(6), ab%(76), ac%(1000) 'p: primes 3 thru 29#/15, c: temporary variable for the calculation of d, d: index of admissible quads in Z/29#Z, o: offsets for sieve, e: change in offsets per 29#, a: 0/1=prime/composite, aa/ab/ac: 0/1=skip sieve in sieving routine below n/y w = Int(k1 / 6469693230#) x = 1 + Int(k2 / 6469693230#) b& = x  w: 'length of search interval 'calculate primes p(1)=3, p(2)=5, ... p(22914109)=431312881  for k2>186e15 the number of primes has to be increased! Cells(1, 4) = "calculate primes below 29#/15... ( 0%)" For q& = 3 To 20759 Step 2 i% = 1 For t& = 3 To Sqr(q&) Step 2 If q& Mod t& = 0 Then i% = 0: t& = Sqr(q&) Next If i% Then j& = j& + 1: p&(j&) = q&: e&(j&) = q&  215656441 Mod q& Next Cells(1, 4) = "calculate primes below 29#/15... ( 1%)" q2& = 1 For q& = 1 To 2338 m& = p&(q&) m& = (m&  1) / 2 For t& = m& + p&(q&) To 215656441 Step p&(q&) a%(t&) = 1 Next If q& = q2& Then q2& = q2& * 4: t1$ = Str$(Int(Sqr(q&) / 0.8)): Cells(1, 4) = "calculate primes below 29#/15... (" + t1$ + "%)" Next Cells(1, 4) = "calculate primes below 29#/15... ( 60%)" For t& = 10385 To 215656441 If a%(t&) = 0 Then j& = j& + 1: p&(j&) = 2 * t& + 1: e&(j&) = p&(j&)  215656441 Mod p&(j&) Next t& = 0 'calculate indexes of admissible quads in Z/29#Z where d=p/30 corresponds to a quadruplet p+{11,13,17,19} (mod 29#) Cells(1, 4) = "calculate admissible quads in Z/29#Z..." d&(0) = 0 d&(1) = 3 d&(2) = 6 dq& = 1 jp& = 30 For n% = 4 To 8 Step 2 q& = 1 jp& = jp& * p&(n%  1) dq& = dq& * (p&(n%  1)  4) For j& = 0 To p&(n%)  1 For k& = 0 To dq&  1 r& = jp& Mod p&(n%) r& = (r& * j& + 30 * d&(k&) + 19) Mod p&(n%) If r& <> 0 And r& <> 2 And r& <> 6 And r& <> 8 Then q& = q& + 1: c&(q&) = jp& / 30 * j& + d&(k&) Next Next q& = 1 jp& = jp& * p&(n%) dq& = dq& * (p&(n%)  4) For j& = 0 To p&(n% + 1)  1 For k& = 0 To dq&  1 r& = jp& Mod p&(n% + 1) r& = (r& * j& + 30 * c&(k&) + 19) Mod p&(n% + 1) If r& <> 0 And r& <> 2 And r& <> 6 And r& <> 8 Then q& = q& + 1: d&(q&) = jp& / 30 * j& + c&(k&) Next Next Next 'estimate time for calculating the offset values l& = Int(Sqr(x * 6469693230#)): 'upper trial division limit t0 = Int((Timer  tm) * l& / 800000000 + 0.5) * 10 If t0 < 90 Then t1$ = " seconds)" Else t0 = Int(t0 / 60 + 0.5): t1$ = " minutes)" 'initialize offset values for sieve in a, where a(1,2,3...n)={0 or 1, quadruplet or at least one composite} correspond to the quad p+{11,13,17,19} where p=30*d(n) (mod 29#) Cells(1, 4) = "calculate offsets for sieve... (this may take about" + Str$(t0) + t1$ j& = 10: 'start at p(10)=31, since all smaller factors are taken care of with the d array Do y = Int(((w  1) * 510510 / p&(j&)  Int((w  1) * 510510 / p&(j&))) * p&(j&) + 0.5) y = Int(((y * 12673 + 29) / p&(j&)  Int((y * 12673 + 29) / p&(j&))) * p&(j&) + 0.5) r& = y: 'the calculation of r=((w1)*29#+29) mod p is split up because I only have 53 bits of precision r& = r& + p&(j&) * (r& Mod 2) pp = p&(j&) For s& = 2 To 30 Step 2 If ((p&(j&) Mod 30) * s&  r& + 18) Mod 30 = 0 Then o&(j&, 1) = 1 + (pp * s&  r& + 18) / 30 If ((p&(j&) Mod 30) * s&  r& + 16) Mod 30 = 0 Then o&(j&, 2) = 1 + (pp * s&  r& + 16) / 30 If ((p&(j&) Mod 30) * s&  r& + 12) Mod 30 = 0 Then o&(j&, 3) = 1 + (pp * s&  r& + 12) / 30 If ((p&(j&) Mod 30) * s&  r& + 10) Mod 30 = 0 Then o&(j&, 4) = 1 + (pp * s&  r& + 10) / 30 Next j& = j& + 1 Loop While p&(j&) < l& 'these are used to speed up the sieving routine below For q& = 0 To 180 Step 30 If q& Mod 7 > 2 Then aa%(q& / 30) = 1 Next For q& = 0 To 2280 Step 30 If q& Mod 7 > 2 Or q& Mod 11 = 0 Or q& Mod 11 = 2 Or q& Mod 11 = 6 Or q& Mod 11 = 8 Then ab%(q& / 30) = 1 Next For q& = 0 To 30000 Step 30 If q& Mod 7 > 2 Or q& Mod 11 = 0 Or q& Mod 11 = 2 Or q& Mod 11 = 6 Or q& Mod 11 = 8 Or q& Mod 13 = 11 Or q& Mod 13 = 0 Or q& Mod 13 = 4 Or q& Mod 13 = 6 Then ac%(q& / 30) = 1 Next sk& = mg& * 2 / 25 'this is for the number of values in d skipped after a quadruplet is found to accelerate the search 'a small overview of the max. difference between sk consecutive values of d vs. the largest possible gap that would be missed: '1000/12782, 2000/25155, 3000/37552, 4000/49958, 5000/62374, 6000/74788, 7000/87080, 8000/99404, 9000/111696, 10000/123987, 15000/185683, 20000/247370, 25000/308830 (ratio approaching 12.3189 = 29#/30/(3*7*9*13*15*19*25)) 'overhead finished, start search in intervals of 6469693230=29# Do Cells(1, 4) = "searching... (k =" + Str$((w + f&) * 6469693230#) + " at a rate of" + Str$(Int(6469.69323 / (Timer  tm))) + "e6 per second)" tm = Timer Erase a%() For m& = 10 To 2047 For nn% = 1 To 4 o&(m&, nn%) = (o&(m&, nn%) + e&(m&)) Mod p&(m&) v& = o&(m&, nn%) For n% = 0 To 1000 If ac%(v& Mod 1001) Then GoTo 1: 'skip sieve when 7, 11 or 13 divides one member of 30d+{11,13,17,19} For k& = v& To 215656441 Step p&(m&) * 1001 a%(k&) = 1 Next 1 v& = v& + p&(m&) Next Next Next For m& = 2048 To 49151 For nn% = 1 To 4 o&(m&, nn%) = (o&(m&, nn%) + e&(m&)) Mod p&(m&) v& = o&(m&, nn%) For n% = 0 To 76 If ab%(v& Mod 77) Then GoTo 2: 'skip sieve when 7 or 11 divides one member of 30d+{11,13,17,19} For k& = v& To 215656441 Step p&(m&) * 77 a%(k&) = 1 Next 2 v& = v& + p&(m&) Next Next Next For m& = 49152 To 786431 For nn% = 1 To 4 o&(m&, nn%) = (o&(m&, nn%) + e&(m&)) Mod p&(m&) v& = o&(m&, nn%) For n% = 0 To 6 If aa%(v& Mod 7) Then GoTo 3: 'skip sieve when 7 divides one member of 30d+{11,13,17,19} For k& = v& To 215656441 Step p&(m&) * 7 a%(k&) = 1 Next 3 v& = v& + p&(m&) Next Next Next For m& = 786432 To j&  1: 'for larger values p(m) the skip (mod 7) as above has no longer an effect w.r.t. speed and can even be counterproductive For nn% = 1 To 4 o&(m&, nn%) = (o&(m&, nn%) + e&(m&)) Mod p&(m&) For k& = o&(m&, nn%) To 215656441 Step p&(m&) a%(k&) = 1 Next Next Next 'sieving done, now looking for gaps For m& = 0 To 17506124 If a%(d&(m&) + 1) = 0 Then g& = d&(m&)  u&: If g& >= mg& Then GoSub 5 Else i% = 0: GoSub 6: 'see below Next f& = f& + 1 If f& Mod 256 = 0 Then ActiveWorkbook.Save: 'saves every 920e6/(throughput in k's per second) minutes Loop While f& <= b& Cells(1, 4) = "finished search in the interval [" + Str$(k1) + "; " + Str$(k2) + " ]" End 'what to do after a quad gap is found 5 If i% = 0 Then GoSub 7: GoTo 6: 'i=0: no jump in m, so no interval left unchecked 'when i=1, there's an unchecked interval t+[1..sk] after a quad 30*d(t)+{11,13,17,19} that has to be examined i% = 0 For q& = t& + sk& To t& + 1 Step 1 If a%(d&(q&) + 1) = 0 Then u& = d&(q&): q& = t& + 1 Next g& = d&(m&)  u& If g& >= mg& Then GoSub 7 6 u& = d&(m&) If m& < 17301504 Then t& = m&: m& = m& + sk&: i% = 1: 'skip some values (sk=mg/12.5, see above) after a quadruplet is found to accelerate the search, but only if an interval overlap is out of question Return 'output gap size and initial quadruplet member p where p=(w+f)*29#+30*(dg)+11 is transformed to a string, else it would show as "1.2345...E+15" and a digit or two would be missed 7 h& = h& + 1: 'line number in the spreadsheet Cells(h&, 1) = g& k0 = w + f& kk$ = Str$(Int(((k0 * 215656441 + d&(m&)  g&) * 30 + 11) / 10000)): 'the four rightmost digits are separated 'error checking routine b/c of possible rounding errors in k0 (compare 5th digit from the right of output value p): kc$ = Str$(Int(((Int((k0 / 100000  Int(k0 / 100000)) * 100000 + 0.5) * 56441 + d&(m&)  g&) * 30 + 11) / 10000)) If Right$(kc$, 1) <> Right$(kk$, 1) Then kk$ = Str$(Val(kk$) + 1) If Right$(kc$, 1) <> Right$(kk$, 1) Then kk$ = Str$(Val(kk$)  2): 'if there's a difference of 1 then it could be either way If Right$(kc$, 1) <> Right$(kk$, 1) Then Cells(h&, 3) = "roundoff error  actual value is ± 10000*n": 'according to my calculations, this should never happen, but please notify me if it does k0 = (Int((k0 / 10000  Int(k0 / 10000)) * 10000 + 0.5) * 6441 + d&(m&)  g&) * 30 + 11 kk$ = kk$ + Right$(Str$(k0), 4): 'attach the four rightmost digits of p Cells(h&, 2) = "'" + kk$ Return Last fiddled with by mart_r on 20200212 at 19:48 
20200213, 16:45  #82 
Feb 2003
11101110001_{2} Posts 
Meanwhile I've found the time to test your VBA code on my workplace PC.
While I'm getting only 550e6/s (indicating that my PC is slower than yours), I can confirm that the two programs are comparable in speed. Moreover, since both programs yield identical results it gives us further confidence that our independent and different algorithms and implementations are both working correctly. 
20200213, 17:53  #83  
Dec 2008
you know...around...
2^{2}·5·29 Posts 
Quote:


20200213, 18:54  #84 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
8627_{10} Posts 

20200214, 08:52  #85  
Feb 2003
11101110001_{2} Posts 
Quote:
The screen freezes and it tells me "the application doesn't respond anymore". But the computations continue and once they are finished, the screen is refreshed and the results are shown. When this happens, one can still minimize the application window, do some other things, and check once in a while whether the computations are finished... 

20200214, 20:35  #86 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
10000110110011_{2} Posts 

20200215, 13:51  #87 
Dec 2008
you know...around...
2^{2}×5×29 Posts 
That's odd. I haven't encountered that behaviour with either Excel 2003, 2010, or 2016. Could you elaborate on the corporate license issues? That also seems new to me, even after more than 20 years of working with Excel.
Something about the nonresponding window though, sometimes when the window doesn't reappear after I click on it on the task bar, I click on and off it while pressing Esc until the VBA window appears where you have the options to stop or continue the calculation. Last fiddled with by mart_r on 20200215 at 13:52 
20200215, 22:49  #88 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
21B3_{16} Posts 
Well, I got a new machine, it runs Win 10. But, rather than running a new version of Excel it runs the older version. Either SysAdmin does not like 365 for security or license issues.
When I tried your code, I opened Excel, AltF11, pasted code in and hit the run button. Poof, excel flat out is gone. Can't test it again for a few days. I won't be at the machine for a while. 
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