# Prime Products just one last time

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### #41 Trurl

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Posted 18 February 2017 - 03:19 AM

I will start the pseudo code.

Notice that an x of 545 is positive and an x test value of 8756 yields a negative.

I am arguing that with these test values the difference from PNP shows if the desired x is higher or lower than the test value.

There is no reason that calculus won’t give a value when limit (equation) when PNP approaches 0. I know it takes more than that but do you agree the pseudo code will show an indication where x will fall at PNP?

Please join this post. If you don’t believe my code, counter it. There should be a pattern in the pseudo-code.

```
x = 545
y = 6737
PNP = 4639* y
(((((x^2*PNP^4 + 2*PNP^2*x^5) + x^8)/
PNP^4) - ((1 - x^2/(2*PNP))))*((PNP^2/x^2)))

545

6737

31252943

(566741960869155702888306342808481973/580236226342089968450)

566741960869155702888306342808481973/580236226342089968450

N[566741960869155702888306342808481973/580236226342089968450, 13]

9.767434971132*10^14

Sqrt[9.76743497113228416002242796713336`13.*^14]

3.125289581964*10^7

PNP - 3.125289581963931252118627996719126077423156917`13.\
301029995663981*^7

47.18036
```

test second x

```
x = 8756
y = 6737
PNP = 4639* y
(((((x^2*PNP^4 + 2*PNP^2*x^5) + x^8)/
PNP^4) - ((1 - x^2/(2*PNP))))*((PNP^2/x^2)))

8756

6737

31252943

73243982077295884748898890760446202375/74884743323939619512464

N[73243982077295884748898890760446202375/74884743323939619512464, 14]

9.7808951231166*10^14

Sqrt[9.780895123116592692523297300191834`14.*^14]

3.1274422653530*10^7

PNP - 3.127442265353046080516318622627538568244967294`14.\
301029995663981*^7

-21479.653530
```

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### #42 Trurl

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Posted 21 April 2017 - 03:50 AM

It is late 20170420…I still stand behind my triangles. You guys are more experienced mathematicians than me. You should have this thing solved already. I know the problem seems erroneous, but good math comes from new ideas. I mean if we always got a clear answer or it was too easy, there would be no point to doing the math. We’d all be English majors. But following is the latest attempt to show the Prime factorization problem may give clues on how to defeat it.

It starts with an equilateral triangle, where all sides equal N.

Then BC is subtracted by CE, where CE = the remainder of N / Pi.

With alternating angles ECD = 30 degrees.

FC = CE/cos(30 degrees).

s = CE, which also equals the remainder of N / Pi.

AEC is similar to syx.

s/AC as x/FC as y/AF.

Otherwise stated: s is proportional to AC as x is proportional the FC

Currently I have not proven all my values. But they are based on a plan and not just random value assignments. Does this intrigue anyone?

No, I am not claiming this works yet. I just wanted some feedback.

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### #43 imatfaal

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Posted 21 April 2017 - 06:43 PM

Even being generous and ignoring the rubbish (remainder when divided by pi?) then this line is demonstrably wrong

FC = CE/cos(30 degrees).

This would only be the case if triangle CEF were a right angled triangle.  It cannot be a right angled triangle as CE is an irrational  number (whole number minus Pi) and BC is a whole number; half a whole number cannot be an irrational

This too..

AEC is similar to syx.

Those triangles would only be similar if lines CE and CF were coincident.  They are not by definition.  This ruins your ratios.

And even though it would be a huge abuse of power - and would be immediately reversed by the other moderators - I will be tempted to suspend you with extreme prejudice if you EVER EVER say that 1 radian equals 60 degrees again.  This is just arrant nonsense.  60 degrees is one sixth of a circle - 1 radian is one (two*pi)th of a circle; surely you understand that this is not the same?

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### #44 Trurl

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Posted 23 April 2017 - 01:34 AM

Even being generous and ignoring the rubbish (remainder when divided by pi?) then this line is demonstrably wrong

We are already in agreement that is wrong. I just didn’t update the drawing. I wanted to show I was using the same drawing. It takes longer to update the drawing.

Those triangles would only be similar if lines CE and CF were coincident.  They are not by definition.  This ruins your ratios.

You are right. I meant to say AFC is similar to syx.

This would only be the case if triangle CEF were a right angled triangle.  It cannot be a right angled triangle as CE is an irrational  number (whole number minus Pi) and BC is a whole number; half a whole number cannot be an irrational

FC = CE/cos(30 degrees) should be:

CE + (CE/cos(30 degrees)) = FC, where CE = s = [remainder of N/PI)

Thanks again for bearing with me as I work through this problem. I will update later with a clearer drawing and definitions. I may seem that I’m an idiot throwing math together. But there is a design around this problem. This geometry might prove to be impossible to solve. Also it is confusing. Be assured that I am not intentionally trying to irritate you with bad math.

I believe these corrections will let you better see how I approached the problem.

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### #45 imatfaal

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Posted 23 April 2017 - 09:22 AM

Similar triangles looks ok from first glance

Not going to bother looking through that dreadful proof page - just grok the distances.  CF is NOT 1.866 times longer than CE.

You cannot uniquely (or even partially) determine triangles with just one angle.  All you know is that angle ECF is 30 degrees - until you can bring some other constraints into your calculations you cannot determine a ratio of side lengths.

Draw a DECENT diagram - with measured angles and lengths and this would be obvious.  Better still spend time at Khan Academy and learn basic maths and geometry before trying to solve one of old problems in subject

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### #46 Trurl

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Posted 8 May 2017 - 10:59 PM

Ok so it looks like my triangle theory has failed. But it doesn’t matter. If an idea does not work it is just a dud.

Here is why I designed the triangle the way I did. S = r * theta. In radians of course, but for the problem I converted it to degrees since my triangle is equilateral. I was looking for a triangle whose sides are proportional to the vector that with resultant of N, where N is the product of 2 Primes.

I theorized that Pi radians or 180 degrees would divide into N and leave the remained of N/Pi (converted to degrees). And from this remainder N – the remainder; and CE = remained of N/Pi = s (on the unknown triangle) would solve the proportions of x and y, where x * y = N.

We agreed that triangle syx was similar to triangle ACE. But I believe that triangle ECD is similar to triangle EBA. Of course, I have not proved it yet, but if true the triangle diagram would be useful.

I began to think about drawing an accurate diagram. I am in the process I just wanted to run the idea by the message board. CE is much smaller part of N than my drawing shows. I am not claiming the triangles are similar, but I am going to do the work to find out.

If this message is hard to understand, give it some leeway. I have not had a class in trig in 20 years. Also, it is difficult to explain why I choose to draw the diagram as I did.

Over the next few weeks I will post the end. Right or wrong. Most likely wrong because of the difficulty of the problem. Even if this idea is a dud, I stand behind my previously posted equations. There is a pattern shown by the equations. It is just unfortunate that it is complex. But my next step will be to simplify the equations. My patterns come out of very simple patterns in multiplication. I want to post the patterns on my website to show how simple they are. I know that N = x *y is supposed to be a one-way function because there are 2 unknowns. However, I don’t believe in one-way functions. Yes, I know I’ve wasted a lot of time on an impossible problem, but it was geometry that gave me a lead. The problem is that no one believes your problem until you can prove it.

So, in a few weeks, I will conclude my work on this ever-confusing drawing and post an improved diagram.

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### #47 imatfaal

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Posted 9 May 2017 - 07:58 AM

Ok so it looks like my triangle theory has failed. But it doesn’t matter. If an idea does not work it is just a dud.

Here is why I designed the triangle the way I did. S = r * theta. In radians of course, but for the problem I converted it to degrees since my triangle is equilateral. I was looking for a triangle whose sides are proportional to the vector that with resultant of N, where N is the product of 2 Primes.

I theorized that Pi radians or 180 degrees would divide into N and leave the remained of N/Pi (converted to degrees). And from this remainder N – the remainder; and CE = remained of N/Pi = s (on the unknown triangle) would solve the proportions of x and y, where x * y = N.

We agreed that triangle syx was similar to triangle ACE. But I believe that triangle ECD is similar to triangle EBA. Of course, I have not proved it yet, but if true the triangle diagram would be useful.

I began to think about drawing an accurate diagram. I am in the process I just wanted to run the idea by the message board. CE is much smaller part of N than my drawing shows. I am not claiming the triangles are similar, but I am going to do the work to find out.

If this message is hard to understand, give it some leeway. I have not had a class in trig in 20 years. Also, it is difficult to explain why I choose to draw the diagram as I did.

Over the next few weeks I will post the end. Right or wrong. Most likely wrong because of the difficulty of the problem. Even if this idea is a dud, I stand behind my previously posted equations. There is a pattern shown by the equations. It is just unfortunate that it is complex. But my next step will be to simplify the equations. My patterns come out of very simple patterns in multiplication. I want to post the patterns on my website to show how simple they are. I know that N = x *y is supposed to be a one-way function because there are 2 unknowns. However, I don’t believe in one-way functions. Yes, I know I’ve wasted a lot of time on an impossible problem, but it was geometry that gave me a lead. The problem is that no one believes your problem until you can prove it.

So, in a few weeks, I will conclude my work on this ever-confusing drawing and post an improved diagram.

I was looking for a triangle whose sides are proportional to the vector that with resultant of N, where N is the product of 2 Primes.

This is initial problem - take any two numbers greater than two and multiply them together and the product will ALWAYS be greater than the sum.  BUT for a triangle the length of two shorter sides must SUM to greater than the third.  This is an internal and irresolvable contradiction.

The long side is the product of the two shorter and thus will be greater than the sum of the two shorter sides BUT AT THE SAME TIME for it to be a properly formed triangle it must also be less than the sum of the two shorter sides.  If you get a contradiction like this you know you must restart with new propositions.

I theorized that Pi radians or 180 degrees would divide into N and leave the remained of N/Pi (converted to degrees). And from this remainder N – the remainder; and CE = remained of N/Pi = s (on the unknown triangle) would solve the proportions of x and y, where x * y = N.

The problem with introducing pi like this is that pi is an irrational number (it is actually transcendental).  An integer multiplied or divided by an irrational will lead to another irrational.  I think - but have not checked - that your construction will have sides all of which will be irrational lengths.  All primes are integers - no primes are irrational

We agreed that triangle syx was similar to triangle ACE. But I believe that triangle ECD is similar to triangle EBA. Of course, I have not proved it yet, but if true the triangle diagram would be useful.

Triangle ECD would be similar to EBA for only one version (ie one possible prime if the idea worked) and that would be when angle ABE equalled angle EDC with both being 60 degrees or 2pi/6.  Angles AEB and CED are equal.  But that is the limit of similarity in the general case

So, in a few weeks, I will conclude my work on this ever-confusing drawing and post an improved diagram.

First things first.  Explain how you will construct triangle - you have three sides explain the relationship between them and your primes.  And let's check you can actually construct a triangle within those parameters.  Remember if the angles are all 60 degrees then you must have equal side lengths - non-negotiable; and vice versa.  Also remember three side lengths uniquely determine a triangle - so that is a good starting point.

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### #48 Trurl

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Posted 11 May 2017 - 12:34 AM

I haven’t confirmed the Prime number part, but the triangles are drawn correctly. The only change is that triangle EDC is a right triangle and for triangle ABE to be similar another 4.789 chord must be drawn at a 30 degree angle from CD. So this new angle is similar. Similar to triangle ABE

4.789 comes from the fact that CE equals [the remainder of (N / Pi ) ] * 85

All of the equilateral sides of the main triangle = N = 85

I have a drawing but it is from AutoCAD 14 and an AutoCad 14 dxf file. I am working to convert.

Also there are 2 more similar triangles.

Triangle BED is similar to triangle AEC

The problem is I can’t find out if triangle BED is also similar to triangle CEF

We know s = CE and triangle syx is similar to triangle AFC

Anyways I am now confused from looking at hundreds of angles. I need help to find if I have enough information to solve triangle AFC.

My drawing is ready. I just have to fight to get it into readable format. This is more difficult than I thought: 32 and 64 bit; AutoCad 14 ; dxf; dwg; So now you will have to believe me that the values work. It really isn't that impressive. Especially unimpressive if I can still not solve for triangle syx as I originally intended to do.

https://1drv.ms/f/s!...Qd7IjIjxkBjv3wz

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### #49 imatfaal

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Posted 11 May 2017 - 02:25 PM

I haven’t confirmed the Prime number part, but the triangles are drawn correctly. The only change is that triangle EDC is a right triangle and for triangle ABE to be similar another 4.789 chord must be drawn at a 30 degree angle from CD. So this new angle is similar. Similar to triangle ABE

4.789 comes from the fact that CE equals [the remainder of (N / Pi ) ] * 85

All of the equilateral sides of the main triangle = N = 85

I have a drawing but it is from AutoCAD 14 and an AutoCad 14 dxf file. I am working to convert.

Also there are 2 more similar triangles.

Triangle BED is similar to triangle AEC

The problem is I can’t find out if triangle BED is also similar to triangle CEF

We know s = CE and triangle syx is similar to triangle AFC

Anyways I am now confused from looking at hundreds of angles. I need help to find if I have enough information to solve triangle AFC.

My drawing is ready. I just have to fight to get it into readable format. This is more difficult than I thought: 32 and 64 bit; AutoCad 14 ; dxf; dwg; So now you will have to believe me that the values work. It really isn't that impressive. Especially unimpressive if I can still not solve for triangle syx as I originally intended to do.

https://1drv.ms/f/s!...Qd7IjIjxkBjv3wz

The only change is that triangle EDC is a right triangle and for triangle ABE to be similar another 4.789 chord must be drawn at a 30 degree angle from CD. So this new angle is similar. Similar to triangle ABE

If EDC is right triangle with Angle EDC (per your autocad) as 90degs then triangle ABE can never be similar.  Angle ABE is 60 degrees, Angle BAE is less than 60, and Angle AEB is the same as Angle CED (and cannot be 90 degrees) .  To summarise EDC is a right triangle and ABE cannot have right angle.  Therefore not similar

Triangle BED is similar to triangle AEC

It is not.  Angle AEC is same as Angle BED.  Angles EAC and DBE are less than 60 degrees.  Angle ACE is 60 degrees thus for triangles to be similar then EDB must be 60 degrees and it is clearly not.

The problem is I can’t find out if triangle BED is also similar to triangle CEF

Think not.  Cannot be bothered to prove

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### #50 Trurl

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Posted 15 May 2017 - 01:31 AM

Think not.

Obviously, you didn’t look at the drawing I posted. This is a science and engineering forum. There must be some viewer who has access to Autocad.

I know you think, I’m stupid claiming to work with Prime numbers. And you don’t think I have a math background. I enjoy you reading my problem and telling me when something just doesn’t work. However, you should have viewed the drawing before dismissing my comments. If I am wrong your judgment is correct. However, there is no wrong. There are wrong techniques, but failures just mean that I try other approaches. In this problem, I am not asking you to find Prime numbers, I am asking the group to find techniques to find triangles with limited given. If you want to reverse a one-way function, you will have to use new ideas, because the old ones don’t work either.

I understand why you think my problem is crap. But don’t think of it as supposed to solve Prime numbers. Think of it as a geometry problem where limited information is known about the angle. Yes, I could be wrong, but I believe I am right-on about the similar angles. The question is does it help me solve the unknown values of the triangle I need.

As you said before a drawing will show everything. I don’t have any programs to draw triangles other than AutoCad 14. The AutoCad 14 files I shared in my last post should open in the current version. I am 20 years behind when it comes to CAD. They are just too expensive to buy. I have the student edition of Solid Works, but I have-to draw as I learn.

So, if you can view my drawing. It may be awhile before I have a drawing in universal format.

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### #51 Strange

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Posted 15 May 2017 - 07:26 AM

As you said before a drawing will show everything. I don’t have any programs to draw triangles other than AutoCad 14.

Microsoft Word? OpenOffice? LibreOffice? Online tools such as Vectr?

So, if you can view my drawing. It may be awhile before I have a drawing in universal format.

You can't export as PDF, GIF, JPG, PS, PNG, TIFF ... ?

Screen grab?

https://forums.autod...bmp/td-p/192390

http://www.zamzar.co...ert/dwg-to-gif/

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### #52 imatfaal

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Posted 15 May 2017 - 10:00 AM

Obviously, you didn’t look at the drawing I posted. This is a science and engineering forum. There must be some viewer who has access to Autocad.

...

I did look at the drawing.  I think the triangles are not necessarily similar (ie there is a circumstance in which they are similar - but most of the time they are not).  Drawings are very misleading if you use them to measure lengths and angles (as you are doing).  You should use diagrams to get your thoughts straight but use geometrical rules to determine things like congruency.

I can draw an equilateral triangle - with enough precision to be confident in it to the full extent of a rough diagram - in about twenty seconds.  Take a picture with a smartphone.  Upload it.

...I know you think, I’m stupid claiming to work with Prime numbers. And you don’t think I have a math background. I enjoy you reading my problem and telling me when something just doesn’t work. However, you should have viewed the drawing before dismissing my comments. If I am wrong your judgment is correct. However, there is no wrong. There are wrong techniques, but failures just mean that I try other approaches. In this problem, I am not asking you to find Prime numbers, I am asking the group to find techniques to find triangles with limited given. If you want to reverse a one-way function, you will have to use new ideas, because the old ones don’t work either...

You are making more assumptions than I did - there is an autocad viewer in the windows 10 appstore.  I viewed your diagram

And there is a wrong. For example; one of yours - if a+b<c  then a,b, and c CANNOT form a triangle and it is wrong to posit the triangle ABC.

We know a huge amount about triangles, constructive and deductive geometry, and, to move on in complexity, trigonometry.  The main problem is that you don't seem to have a good grounding in this.

...I understand why you think my problem is crap. But don’t think of it as supposed to solve Prime numbers. Think of it as a geometry problem where limited information is known about the angle. Yes, I could be wrong, but I believe I am right-on about the similar angles. The question is does it help me solve the unknown values of the triangle I need...

But as a geometry puzzle it lacks precision - everyone reading it should be able to reproduce the construction easily but this is not possible because you chance the rules when some part is proven to be wrong

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### #53 Trurl

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Posted 19 May 2017 - 11:22 PM

You sound like you have some good math wisdom. I value your comments. I will have to evaluate the use of this geometric diagram.

I didn't know there was a AutoCad viewer in Windows 10 store. I didn't know people actually used the store. I'll have to check it out.

Anyways I was wrong. You did give a fair view of my problem. I misunderstood you comments about viewing the drawing. I have claimed in many posts ago on a different thread that I could solve SSA (side, side, angle). I did not want to bring that back up. But later I watch a math video on "The Great Courses" that the mathematician said he could solve SSA with some obtuse triangles. That is if I understood him right. This problem is not based on that. But again it is trying to find triangles knowing only 2 sides, with certain conditions known by other triangles.

The following is not a religious statement. But in Christianity an non-believer would say if God is so strong can he make a boulder that he can't lift? If he can't he isn't all powerful. But you could extend it to this problem. If God is so powerful can he make a one-way function even he can't reverse? So do one-way functions exist?

I believe as humans we are limited and one-way functions do exist. Knowing only N and finding 2 unknowns, knowing only a slight process in which N was encoded is a difficult if not impossible task.

I have been working on this problem for a long time. I took a break to study Amateur Radio. But I would like to share the patterns in the multiplication I have found and based my equations. They are simplistic but I have to go through and list them all. Maybe someone will see something I missed.

Anyways thanks for the comments. I don't always like being wrong, but I think it is more about being realistic with this problem. I don't know. Would you be interested in seeing a 5 step pattern in multiplication?

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### #54 imatfaal

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Posted 20 May 2017 - 04:03 PM

...

Anyways I was wrong. You did give a fair view of my problem. I misunderstood you comments about viewing the drawing. I have claimed in many posts ago on a different thread that I could solve SSA (side, side, angle). I did not want to bring that back up. But later I watch a math video on "The Great Courses" that the mathematician said he could solve SSA with some obtuse triangles. That is if I understood him right. This problem is not based on that. But again it is trying to find triangles knowing only 2 sides, with certain conditions known by other triangles.

Yes - I understand that; you need to get your head around what can be done and what cannot.  There are numerous texts on this sort of geometrical conundrum.  Which angles are equal, supplementary, complementary  and which lines are parallel.  Most of this can be done with a careful diagram done with ruler and compass.  You can get to trigonometry and cosine and sine rules - but then you also have to consider that triangles with whole number sides (primes remember) are a requirement.

Have you actually tried constructing triangles with known primes - you obviously haven't because your early assertions to the numbers required were impossible.  I presume you know how to construct a rough triangle with a straight edge, ruler, and compasses

The following is not a religious statement. But in Christianity an non-believer would say if God is so strong can he make a boulder that he can't lift? If he can't he isn't all powerful. But you could extend it to this problem. If God is so powerful can he make a one-way function even he can't reverse? So do one-way functions exist?

Sounds like chop-logic and apologia to me And a real non-believer wouldn't say that - because God is a supernatural entity with no proof anyway so why introduce other complications.  Personally I think it is a strange question - and you are not the first person to have mentioned it; the question strikes me as incredible hubris.  We postulate a supernatural being who by very existence/definition must transcend human bounds and understanding; yet immediately we bring in human constraints and frailties.   But this is not the place

I believe as humans we are limited and one-way functions do exist. Knowing only N and finding 2 unknowns, knowing only a slight process in which N was encoded is a difficult if not impossible task...

It is not merely that humans are limited - it is that maths is axiomatic.  We make the foundations of our maths and build from there; within those axioms we can say what is true (sometimes), what is false (sometimes), and what we cannot decide upon (sometimes).  Whilst some things are not decidable; if we can prove it within the system of axioms then it is proven and nothing can change that

Anyways thanks for the comments. I don't always like being wrong, but I think it is more about being realistic with this problem. I don't know. Would you be interested in seeing a 5 step pattern in multiplication?

No one likes being wrong - that's why we study and learn.  You are right about doses of realism; you are tackling Mount Everest and getting angry with yourself that a short walk every evening hasn't been enough training.  This is an stubborn peak of mathematics that the greatest thinkers have pushed themselves to the limit in an effort to make that vital breakthrough.  You are using tools that have been thoroughly tested by people like Euclid, Fermat, and Leibnitz; you can be virtually certain there are no simple things that will crack prime numbers.

That is the benefit of fora - post stuff when you have time; someone will look at and critique your 5 step pattern.  There are numerous posts in this subforum about the patterns of multiples which are ruled out from being prime

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### #55 Trurl

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Posted 24 May 2017 - 12:07 AM

I think this problem needs a rest for awhile.

I just wanted to post my CAD drawings. They come straight from the Wiki-leaks exploits and are For Internal Use Only.

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