20200124, 00:37  #177 
Jun 2015
Vallejo, CA/.
3BC_{16} Posts 

20200124, 22:49  #178  
May 2018
2·3·31 Posts 
Quote:


20200126, 10:33  #179  
Jun 2003
Oxford, UK
3×5^{4} Posts 
Quote:
I will repeat for the third time, I am not saying this gap has a record merit. I am saying 211 is the upper prime of a record merit for all gaps <=12 between primes. You can argue that there is a gap between 113 and 125 which is the same length, but this is not a gap between primes, and the gap between 113 and 127 is larger than 12. Last fiddled with by robert44444uk on 20200126 at 10:34 

20200128, 15:26  #180 
Random Account
Aug 2009
U.S.A.
2344_{8} Posts 

20200128, 19:34  #181  
Dec 2008
you know...around...
3^{2}×61 Posts 
Quote:
Quote:
Anyway, I've attached the data for k<7e15, where the maximum gaps are simply marked with an asterisk, like in the tables of Dr. Nicely. There are yet no 5000+ gaps in my current search range. ________ Since at my workplace we're not allowed to run external programs, I took the time to put together my own VBA program that runs in an MS Excel environment. I was pretty delighted to discover that it runs on a decent speed of about 23e6 k's per core per second (Core i5 @ 3.00 GHz). A bit disappointed though that, while trying it out at home, it's only one third of the speed of the Perl program (well, depending on the architecture, YMMV  maybe someone else can gather more data on timings, I'm still in the process of doing so). Still, for me being only a mediocre programmer and I've been told that VBA was slow, that ought to be quite something. The program is merely a variant of SOE, and utilizes about 700 MB of RAM. Is it faster to do only a bit of trial division, as it were, and run a probable prime test on the remaining candidates (like I did in Pari) or work with trial division all along the way (like i did here)? Maybe, just maybe, this can be compiled/optimized to the point where it's faster than the current C program? Code:
'init k1=start value, k2=end value, mg=mingap report k1 = 7E+15 k2 = 7.000123E+15 mg& = 3072 tm = Timer Cells(1, 1) = "initializing..." Dim p&(16252324), c&(378675), d&(7952175), o&(16252324, 2), e&(16252324), a%(185910725) 'p: primes 3 thru 3*10^8, c: temporary variable for the calculation of d, d: index of admissible twins in Z/23#Z, o: offsets for sieve, e: change in offsets per 5*23#, a: 0/1=prime/composite w = Int(6 * k1 / 223092870) x = 1 + Int(6 * k2 / 223092870) b& = x  w: 'length of search interval 'calculate primes p(1)=3, p(2)=5, ... p(16252324)=299999977  for k2>1.5e16 the number of primes has to be increased! Currently limited to 2^31/6 ~ 3.58e8, thus the program is currently limited to k<2.135e16. Can be scaled up in the routine below marked with *) For q& = 3 To 17317 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&  185910725 Mod q& Next For q& = 1 To 1989 m& = p&(q&) m& = (m&  1) / 2 For t& = m& + p&(q&) To 150000000 Step p&(q&) a%(t&) = 1 Next Next For t& = 8660 To 150000000 If a%(t&) = 0 Then j& = j& + 1: p&(j&) = 2 * t& + 1: e&(j&) = p&(j&)  185910725 Mod p&(j&) Next 'calculate indexes of admissible twins in Z/23#Z where d=p/6 corresponds to a twin p±1 (mod 23#) d&(1) = 2 d&(2) = 3 d&(3) = 5 q& = 0 For j& = 0 To 6 For k& = 1 To 3 r& = (30 * j& + 6 * d&(k&) + 1) Mod 7 If r& <> 0 And r& <> 2 Then q& = q& + 1: c&(q&) = 5 * j& + d&(k&) Next Next q& = 0 For j& = 0 To 10 For k& = 1 To 15 r& = (210 * j& + 6 * c&(k&) + 1) Mod 11 If r& <> 0 And r& <> 2 Then q& = q& + 1: d&(q&) = 35 * j& + c&(k&) Next Next q& = 0 For j& = 0 To 12 For k& = 1 To 135 r& = (2310 * j& + 6 * d&(k&) + 1) Mod 13 If r& <> 0 And r& <> 2 Then q& = q& + 1: c&(q&) = 385 * j& + d&(k&) Next Next q& = 0 For j& = 0 To 16 For k& = 1 To 1485 r& = (30030 * j& + 6 * c&(k&) + 1) Mod 17 If r& <> 0 And r& <> 2 Then q& = q& + 1: d&(q&) = 5005 * j& + c&(k&) Next Next q& = 0 For j& = 0 To 18 For k& = 1 To 22275 r& = (510510 * j& + 6 * d&(k&) + 1) Mod 19 If r& <> 0 And r& <> 2 Then q& = q& + 1: c&(q&) = 85085 * j& + d&(k&) Next Next q& = 0 For j& = 0 To 22 For k& = 1 To 378675 r& = (9699690 * j& + 6 * c&(k&) + 1) Mod 23 If r& <> 0 And r& <> 2 Then q& = q& + 1: d&(q&) = 1616615 * j& + c&(k&) Next Next 'initialize offset values for sieve in a, where a(1,2,3...)={0 or 1, twin prime or either p1 or p+1 composite} correspond to the twin p±1 where p=6*a (mod 23#) l& = Int(Sqr(x * 223092870)): 'upper trial division limit j& = 9: 'start at p(9)=29, since all smaller factors are taken care of with the d array Do y = Int(((w  5) * 30030 / p&(j&)  Int((w  5) * 30030 / p&(j&))) * p&(j&) + 0.5) y = Int(((y * 7429 + 23) / p&(j&)  Int((y * 7429 + 23) / p&(j&))) * p&(j&) + 0.5) r& = y: 'the calculation of r=((w5)*23#+23) mod p is split up because I only have 53 bits of precision r& = r& + p&(j&) * (r& Mod 2) For s& = 2 To 6 Step 2: '*) this loop must be changed if primes p>2^31/6 are employed If (p&(j&) * s&  r&) Mod 6 = 0 Then o&(j&, 1) = 4 + (p&(j&) * s&  r&) / 6 If (p&(j&) * s&  r&  2) Mod 6 = 0 Then o&(j&, 2) = 4 + (p&(j&) * s&  r&  2) / 6 Next j& = j& + 1 Loop While p&(j&) < l& 'overhead finished, start search in intervals of 1115464350=5*23# (if MS allows it, I might push the envelope here and make the intervals even larger) Do Cells(h& + 1, 1) = "searching... (k =" + Str$((w + f&) * 37182145) + " at a rate of" + Str$(Int(185910725 / (Timer  tm))) + " k's per second)" tm = Timer Erase a%() For m& = 9 To 262143 o&(m&, 1) = (o&(m&, 1) + e&(m&)) Mod p&(m&) o&(m&, 2) = (o&(m&, 2) + e&(m&)) Mod p&(m&) v& = o&(m&, 1) For n% = 0 To 4 If v& Mod 5 = 1 Or v& Mod 5 = 4 Then GoTo 1: 'skip sieve when 5 divides one member of 6d±1; could do it also for 7, but that probably makes the routine unwieldy and thus slower (someone might check that though) For k& = v& To 185910725 Step p&(m&) * 5 a%(k&) = 1 Next 1 v& = v& + p&(m&) Next v& = o&(m&, 2) For n% = 0 To 4 If v& Mod 5 = 1 Or v& Mod 5 = 4 Then GoTo 2 For k& = v& To 185910725 Step p&(m&) * 5 a%(k&) = 1 Next 2 v& = v& + p&(m&) Next Next For m& = 262144 To j&  1: ' for larger values p&(m&) the skip (mod 5) as above has no longer an effect w.r.t. speed and can even be counterproductive o&(m&, 1) = (o&(m&, 1) + e&(m&)) Mod p&(m&) o&(m&, 2) = (o&(m&, 2) + e&(m&)) Mod p&(m&) For k& = o&(m&, 1) To 185910725 Step p&(m&) a%(k&) = 1 Next For k& = o&(m&, 2) To 185910725 Step p&(m&) a%(k&) = 1 Next Next 'sieving done, now looking for gaps v& = 0 For n% = 0 To 4 For m& = 1 To 7952175 If a%(d&(m&) + v&) = 0 Then g& = d&(m&)  u&: u& = d&(m&): If g& >= mg& Then h& = h& + 1: Cells(h&, 1) = g&: Cells(h&, 2) = Str$(w + f& + n%) + " * 23#/6 +" + Str$(d&(m&)  g&) Next 'TBD: skip m by 0.7~0.8*mg after a twin, subroutine ensues, but since the sieving requires 93% of the calc time and the search in a% only 7%, the overall speedup shouldn't be too significant, possibly about 5% 'also TBD: output k as a whole number, maybe next week... u& = u&  37182145 v& = v& + 37182145 Next f& = f& + 5 If f& Mod 256 = 0 Then ActiveWorkbook.Save: 'saves every 793e6/(throughput in k's per second) minutes Loop While f& <= b& Cells(h& + 1, 1) = "finished search in the interval [" + Str$(k1) + "; " + Str$(k2) + " ]" 

20200129, 01:02  #182 
Random Account
Aug 2009
U.S.A.
2^{2}·313 Posts 

20200129, 03:00  #183 
"Curtis"
Feb 2005
Riverside, CA
3×5×281 Posts 

20200129, 17:07  #184  
Random Account
Aug 2009
U.S.A.
2^{2}·313 Posts 
Quote:
Riesel: Is this not a strict format of 5*2^x1? It seems this would dry up rapidly with lots of people working on it. 

20200203, 21:34  #185 
Dec 2008
you know...around...
3^{2}×61 Posts 
Twin prime gap search program for Excel/VBA
There, I sped my program up by almost 30%
If C or Perl is not an option for anybody, maybe this will do it? Code:
'k1=start value, k2=end value, mg=mingap report ' k1 = 7.492811E+15 k2 = 7.492812E+15 mg& = 4096 ' '(come think of it, I could use an input box here...) tm = Timer Cells(1, 1) = "initializing... (may take a couple of seconds)" Dim p&(16252324), c&(378675), d&(7952175), o&(16252324, 2), e&(16252324), a%(185910725), aa%(34) 'p: primes 3 thru 3*10^8, c: temporary variable for the calculation of d, d: index of admissible twins in Z/23#Z, o: offsets for sieve, e: change in offsets per 5*23#, a: 0/1=prime/composite, aa: 0/1=skip sieve in sieving routine below n/y w = Int(6 * k1 / 223092870) x = 1 + Int(6 * k2 / 223092870) b& = x  w: 'length of search interval 'calculate primes p(1)=3, p(2)=5, ... p(16252324)=299999977  for k2>1.5e16 the number of primes has to be increased! Currently limited to 2^31/6 ~ 3.58e8, thus the program is currently limited to k<2.135e16. Can be scaled up in the routine below marked with *) For q& = 3 To 17317 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&  185910725 Mod q& Next For q& = 1 To 1989 m& = p&(q&) m& = (m&  1) / 2 For t& = m& + p&(q&) To 150000000 Step p&(q&) a%(t&) = 1 Next Next For t& = 8660 To 150000000 If a%(t&) = 0 Then j& = j& + 1: p&(j&) = 2 * t& + 1: e&(j&) = p&(j&)  185910725 Mod p&(j&) Next 'calculate indexes of admissible twins in Z/23#Z where d=p/6 corresponds to a twin p±1 (mod 23#) d&(1) = 2 d&(2) = 3 d&(3) = 5 q& = 0 For j& = 0 To 6 For k& = 1 To 3 r& = (30 * j& + 6 * d&(k&) + 1) Mod 7 If r& <> 0 And r& <> 2 Then q& = q& + 1: c&(q&) = 5 * j& + d&(k&) Next Next q& = 0 For j& = 0 To 10 For k& = 1 To 15 r& = (210 * j& + 6 * c&(k&) + 1) Mod 11 If r& <> 0 And r& <> 2 Then q& = q& + 1: d&(q&) = 35 * j& + c&(k&) Next Next q& = 0 For j& = 0 To 12 For k& = 1 To 135 r& = (2310 * j& + 6 * d&(k&) + 1) Mod 13 If r& <> 0 And r& <> 2 Then q& = q& + 1: c&(q&) = 385 * j& + d&(k&) Next Next q& = 0 For j& = 0 To 16 For k& = 1 To 1485 r& = (30030 * j& + 6 * c&(k&) + 1) Mod 17 If r& <> 0 And r& <> 2 Then q& = q& + 1: d&(q&) = 5005 * j& + c&(k&) Next Next q& = 0 For j& = 0 To 18 For k& = 1 To 22275 r& = (510510 * j& + 6 * d&(k&) + 1) Mod 19 If r& <> 0 And r& <> 2 Then q& = q& + 1: c&(q&) = 85085 * j& + d&(k&) Next Next q& = 0 For j& = 0 To 22 For k& = 1 To 378675 r& = (9699690 * j& + 6 * c&(k&) + 1) Mod 23 If r& <> 0 And r& <> 2 Then q& = q& + 1: d&(q&) = 1616615 * j& + c&(k&) Next Next 'initialize offset values for sieve in a, where a(1,2,3...)={0 or 1, twin prime or either p1 or p+1 composite} correspond to the twin p±1 where p=6*a (mod 23#) l& = Int(Sqr(x * 223092870)): 'upper trial division limit j& = 9: 'start at p(9)=29, since all smaller factors are taken care of with the d array Do y = Int(((w  5) * 30030 / p&(j&)  Int((w  5) * 30030 / p&(j&))) * p&(j&) + 0.5) y = Int(((y * 7429 + 23) / p&(j&)  Int((y * 7429 + 23) / p&(j&))) * p&(j&) + 0.5) r& = y: 'the calculation of r=((w5)*23#+23) mod p is split up because I only have 53 bits of precision r& = r& + p&(j&) * (r& Mod 2) For s& = 2 To 6 Step 2: '*) this loop must be changed if primes p>2^31/6 are employed If (p&(j&) * s&  r&) Mod 6 = 0 Then o&(j&, 1) = 4 + (p&(j&) * s&  r&) / 6 If (p&(j&) * s&  r&  2) Mod 6 = 0 Then o&(j&, 2) = 4 + (p&(j&) * s&  r&  2) / 6 Next j& = j& + 1 Loop While p&(j&) < l& 'these are used to speed up the sieving routine below For q& = 0 To 204 Step 6 If q& Mod 5 = 1 Or q& Mod 5 = 4 Or q& Mod 7 = 1 Or q& Mod 7 = 6 Then aa%(q& / 6) = 1 Else aa%(q& / 6) = 0 Next 'overhead finished, start search in intervals of 1115464350=5*23# (if MS allows it, I might push the envelope here and make the intervals even larger) Do Cells(h& + 1, 1) = "searching... (k =" + Str$((w + f&) * 37182145) + " at a rate of" + Str$(Int(185910725 / (Timer  tm))) + " k's per second)" tm = Timer Erase a%() For m& = 9 To 65535 o&(m&, 1) = (o&(m&, 1) + e&(m&)) Mod p&(m&) o&(m&, 2) = (o&(m&, 2) + e&(m&)) Mod p&(m&) v& = o&(m&, 1) For n% = 0 To 34 If aa%(v& Mod 35) Then GoTo 1: 'skip sieve when 5 or 7 divides one member of 6d±1 For k& = v& To 185910725 Step p&(m&) * 35 a%(k&) = 1 Next 1 v& = v& + p&(m&) Next v& = o&(m&, 2) For n% = 0 To 34 If aa%(v& Mod 35) Then GoTo 2 For k& = v& To 185910725 Step p&(m&) * 35 a%(k&) = 1 Next 2 v& = v& + p&(m&) Next Next For m& = 65536 To 393215 o&(m&, 1) = (o&(m&, 1) + e&(m&)) Mod p&(m&) o&(m&, 2) = (o&(m&, 2) + e&(m&)) Mod p&(m&) v& = o&(m&, 1) For n% = 0 To 4 If aa%(v& Mod 5) Then GoTo 3: 'skip sieve when 5 divides one member of 6d±1 For k& = v& To 185910725 Step p&(m&) * 5 a%(k&) = 1 Next 3 v& = v& + p&(m&) Next v& = o&(m&, 2) For n% = 0 To 4 If aa%(v& Mod 5) Then GoTo 4 For k& = v& To 185910725 Step p&(m&) * 5 a%(k&) = 1 Next 4 v& = v& + p&(m&) Next Next For m& = 393216 To j&  1: ' for larger values p&(m&) the skip (mod 5) as above has no longer an effect w.r.t. speed and can even be counterproductive o&(m&, 1) = (o&(m&, 1) + e&(m&)) Mod p&(m&) o&(m&, 2) = (o&(m&, 2) + e&(m&)) Mod p&(m&) For k& = o&(m&, 1) To 185910725 Step p&(m&) a%(k&) = 1 Next For k& = o&(m&, 2) To 185910725 Step p&(m&) a%(k&) = 1 Next Next 'sieving done, now looking for gaps v& = 0 For n% = 0 To 4 For m& = 1 To 7952175 If a%(d&(m&) + v&) = 0 Then g& = d&(m&)  u&: If g& >= mg& Then GoSub 5 Else i% = 0: GoSub 6: 'see below Next 'TBD: output k as a whole number, maybe next week... u& = u&  37182145 v& = v& + 37182145 Next f& = f& + 5 If f& Mod 256 = 0 Then ActiveWorkbook.Save: 'saves every 793e6/(throughput in k's per second) minutes Loop While f& <= b& Cells(h& + 1, 1) = "finished search in the interval [" + Str$(k1) + "; " + Str$(k2) + " ]" End 5 If i% = 0 Then h& = h& + 1: Cells(h&, 1) = g&: Cells(h&, 2) = Str$(w + f& + n%) + " * 23#/6 +" + Str$(d&(m&)  g&): GoTo 6: 'i%=0: no jump in m, so no interval left unchecked 'when i%=1, there's an unchecked interval t+[1..320] after a twin 6*d(t)± 1 that has to be examined i% = 0 For q& = t& + 320 To t& + 1 Step 1 If a%(d&(q&) + v&) = 0 Then u& = d&(q&): q& = t& + 1 Next g& = d&(m&)  u& If g& >= mg& Then h& = h& + 1: Cells(h&, 1) = g&: Cells(h&, 2) = Str$(w + f& + n%) + " * 23#/6 +" + Str$(d&(m&)  g&) 6 u& = d&(m&) If m& < 7946240 Then t& = m&: m& = m& + 320: i% = 1: 'skip some values after a twin is found to accelerate the search, but only if an interval overlap is out of question Return 
20200204, 00:27  #186  
Einyen
Dec 2003
Denmark
2×1,429 Posts 
Quote:
https://en.wikipedia.org/wiki/Lucas%...%93Riesel_test (LLR) Proth numbers are of the form k*2^{n} + 1 and k<2^{n} https://en.wikipedia.org/wiki/Proth%27s_theorem and the corresponding software to run the test is Proth: https://github.com/galloty/proth20 

20200212, 20:20  #187 
Dec 2008
you know...around...
1000100101_{2} Posts 
Reserving 7.5e15 to 8e15.
Nothing special in my previous range, only one 5000+ gap: Code:
5103 7181481105338907 I'll update the tables once I finished this new range. 
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