Mathematical proof turned down by JAMS.

[Rudy Toody]

Originally posted by: Born2bwire
You should spend some time reading the papers in the journal(s) you wish to submit (and other journals on the same subject) to be more aware of the kinds of papers they publish and the standards.

I realize that now. When I was writing fiction, I would study the market for my kind of stuff and format everything for the specific magazine

I don't know why I didn't do something like that for this work.

I just ordered "Proofs From the Book," that contains a number of notable proofs. I should get a good introduction to a variety of notable methods.

Meanwhile, I am creating a few more exhibits that might be included in a paper.

 

[Rudy Toody]

I knew if I posted this in a place where a lot of smart people hang out that I would experience a thoughtful and stimulating discussion! Terrific, guys!

Based on what I have learned so far, we are riding a dead horse! There is not enough information in this sieve to prove much of anything.

However, I have just had another golden moment and have come up with a better sieve that provides much more infomation. It is quite complex, so it will be a week or so before I complete the mapping to Euler's Sieve. When I complete it, I will post the specs, (with examples), on this forum in a new thread with a llink to this one

I want to thank everyone for their patience with a neophyte mathematician. I'll see you in about a week. Meanwhile, I will keep checking this thread for more insights.

 

[Cogman]

Good luck, Who knows, you may crack one of the over 100 year old mysteries. If so, that would be pretty cool.

 

[TuxDave]

Half of me is happy to read such high level discussions....

The other half is unhappy because my brain froze trying to read it.

 

[Schmide]

Every mathematician chases many gooses to catch one gosling.

 

[Cogman]

Originally posted by: Schmide
Every mathematician chases many gooses to catch one gosling.

whats a gooses? Unless you really ment

3 plural goos·es : a tailor's smoothing iron with a gooseneck handle
4 plural goos·es : a poke between the buttocks

#4 being the funniest [/anal english mode] (The plural for goose is geese).

 

[DrPizza]

I'll be more blunt, sorry. Here's how they probably decided in less than one day:
"I prove the supply of twin primes is infinite..." "WHOA! OMG, and this is only one page!"
<skim><skim><skim>
"by definition there are infinite primes" "???!! wtf?"

"this is nonsense, the person shows a complete lack of knowledge in this field." As soon as any math journal editor saw that line, your paper was ignored. They simply don't have the time, nor manpower to carefully go through the rest of your paper to see if there are any tidbits that would shed new light on the search for a proof.

However, your twin prime sieve may be something new, or you may have simply rediscovered something that's been independently discovered many times before. I'd recommend searching online for twin prime sieves and trying to assess if yours truly is novel. If that's the case, the determine the proper style to write your paper & resubmit it. Kudos to your efforts though.

edit: skimmed through the thread & missed your last post. If you have a better sieve, that would be awesome. It'll be even more awesome if it's something new to the math world. It's amazing how many ideas have already been published though. Good luck!

 

[Cogman]

Originally posted by: DrPizza
I'll be more blunt, sorry. Here's how they probably decided in less than one day:
"I prove the supply of twin primes is infinite..." "WHOA! OMG, and this is only one page!"
<skim><skim><skim>
"by definition there are infinite primes" "???!! wtf?"

"this is nonsense, the person shows a complete lack of knowledge in this field." As soon as any math journal editor saw that line, your paper was ignored. They simply don't have the time, nor manpower to carefully go through the rest of your paper to see if there are any tidbits that would shed new light on the search for a proof.

However, your twin prime sieve may be something new, or you may have simply rediscovered something that's been independently discovered many times before. I'd recommend searching online for twin prime sieves and trying to assess if yours truly is novel. If that's the case, the determine the proper style to write your paper & resubmit it. Kudos to your efforts though.

edit: skimmed through the thread & missed your last post. If you have a better sieve, that would be awesome. It'll be even more awesome if it's something new to the math world. It's amazing how many ideas have already been published though. Good luck!

Yeah, the wording is off there (as there is no definition that says there are infinite primes) but that really wasn't the biggest problem. I worry about the wording of things last, the actual proof first.

 

[Rudy Toody]

I was so excited to discover the sieve that I got carried away in my haste to get it published. The sieve is truly new and novel. There is nothing like it in the published literature. That's why I submitted it.

I agree with Cogman, the proof should come first and then formatting per some style sheet should be almost the last step.

I thought the last step would be posing for pictures.

 

[Estrella]

Originally posted by: Rudy Toody
I was so excited to discover the sieve that I got carried away in my haste to get it published. The sieve is truly new and novel. There is nothing like it in the published literature. That's why I submitted it.

I agree with Cogman, the proof should come first and then formatting per some style sheet should be almost the last step.

I thought the last step would be posing for pictures.

I know I am being a bit nit-picky but, what is it that you consider the literature? Is that all the Number Theory journals or something even more substantive?

 

[silverpig]

I know a couple of mathematician friends (ie, non-professors) who could look at your next attempt and advise you a little bit. They might even be able to pass it on to someone with a reputation to help you get it published...

 

[Rudy Toody]

Originally posted by: Estrella
I know I am being a bit nit-picky but, what is it that you consider the literature? Is that all the Number Theory journals or something even more substantive?

I consider the literature to be everything published and available to the public.

Whatever I read, I chase the references to learn more. Then I chased those references.

For example: When I was a sophmore in high schooi, I decided to read every book ever written about parapsychology. I chased every book that was referenced by another book. I considered books that had no references to be of no value¹. By this process, I found every book. (In this case, I determined that there were too many circular references and not enough original research to convince me that parapsychology had any merit),

¹ Oops! I guess that submitting a math paper that has no references falls into that category.

Edit: Christopher Columbus used this method on the Flat Earth Conjecture.
Edit2: I just received Proofs from THE BOOK by Martin Aigner and G&uuml;nter M. Ziegler, Second Edition

From the preface:

Paul Erd&ouml;s liked to talk about The Book, is which God maintains the perfect proofs for mathematical theorems. following the dictum of G. H. Hardy that there is no permanant place for ugly mathematics.

The first chapter contains 6 proofs of the infinity of primes--from Euclid forward.

In my citations, could I cite this book as the source for a proof. Or, should I email Euclid to get a copy of his?

 

[Estrella]

Originally posted by: Rudy Toody

Originally posted by: Estrella
I know I am being a bit nit-picky but, what is it that you consider the literature? Is that all the Number Theory journals or something even more substantive?

I consider the literature to be everything published and available to the public.

Whatever I read, I chase the references to learn more. Then I chased those references.

For example: When I was a sophmore in high schooi, I decided to read every book ever written about parapsychology. I chased every book that was referenced by another book. I considered books that had no references to be of no value¹. By this process, I found every book. (In this case, I determined that there were too many circular references and not enough original research to convince me that parapsychology had any merit),

¹ Oops! I guess that submitting a math paper that has no references falls into that category.

Edit: Christopher Columbus used this method on the Flat Earth Conjecture.
Edit2: I just received Proofs from THE BOOK by Martin Aigner and Günter M. Ziegler, Second Edition

From the preface:

Paul Erdös liked to talk about The Book, is which God maintains the perfect proofs for mathematical theorems. following the dictum of G. H. Hardy that there is no permanant place for ugly mathematics.

The first chapter contains 6 proofs of the infinity of primes--from Euclid forward.

In my citations, could I cite this book as the source for a proof. Or, should I email Euclid to get a copy of his?

As I critique your paper I will assume you are right and I will only provide insight into how to write your paper.

Some General Rules:

1. In a scholarly math paper do not enumerate steps as you did in "Modified Steps of Euler's Sieve". Instead, you should use paragraphs which show clear logic. Every part of your argument should flow from what came before it.

2. Use notation SPARINGLY. Mathematical shorthand such as: for every, there exists, subset of whatever set, etc.; should be left on the blackboard or in your notebook.

3. Make sure your citations are at the end of the paper in a clearly marked section. You should cite by whatever the current MLA standards are.

4. Whenever you say by definition, it must be the actual definition. For instance you say,"By definition: There are infinite primes." There are not infinite primes by definition. There is a theorem which states such but, not a definition.

Yes, there are a lot of other rules too. I know I did not write nearly everything.

Now, I can tell you exactly why your paper was rejected in probably less than thirty seconds. At 1 in the Modified Steps of Euler's Sieve,"Create set N of natural numbers from 1 to infinity." One cannot create the set of Natural numbers. If you honestly think you can, then take a sheet of paper and start writing all of the Natural numbers (seriously don't).

Secondly, what I said in general rules about your letter a in "The Proof".

Here is a paper you should be able to understand and is written correctly,"Groups as the Union of Subgroups".

 

[Cogman]

Originally posted by: Estrella

Originally posted by: Rudy Toody

Originally posted by: Estrella
I know I am being a bit nit-picky but, what is it that you consider the literature? Is that all the Number Theory journals or something even more substantive?

I consider the literature to be everything published and available to the public.

Whatever I read, I chase the references to learn more. Then I chased those references.

For example: When I was a sophmore in high schooi, I decided to read every book ever written about parapsychology. I chased every book that was referenced by another book. I considered books that had no references to be of no value¹. By this process, I found every book. (In this case, I determined that there were too many circular references and not enough original research to convince me that parapsychology had any merit),

¹ Oops! I guess that submitting a math paper that has no references falls into that category.

Edit: Christopher Columbus used this method on the Flat Earth Conjecture.
Edit2: I just received Proofs from THE BOOK by Martin Aigner and Günter M. Ziegler, Second Edition

From the preface:

Paul Erdös liked to talk about The Book, is which God maintains the perfect proofs for mathematical theorems. following the dictum of G. H. Hardy that there is no permanant place for ugly mathematics.

The first chapter contains 6 proofs of the infinity of primes--from Euclid forward.

In my citations, could I cite this book as the source for a proof. Or, should I email Euclid to get a copy of his?

As I critique your paper I will assume you are right and I will only provide insight into how to write your paper.

Some General Rules:

1. In a scholarly math paper do not enumerate steps as you did in "Modified Steps of Euler's Sieve". Instead, you should use paragraphs which show clear logic. Every part of your argument should flow from what came before it.

2. Use notation SPARINGLY. Mathematical shorthand such as: for every, there exists, subset of whatever set, etc.; should be left on the blackboard or in your notebook.

3. Make sure your citations are at the end of the paper in a clearly marked section. You should cite by whatever the current MLA standards are.

4. Whenever you say by definition, it must be the actual definition. For instance you say,"By definition: There are infinite primes." There are not infinite primes by definition. There is a theorem which states such but, not a definition.

Yes, there are a lot of other rules too. I know I did not write nearly everything.

Now, I can tell you exactly why your paper was rejected in probably less than thirty seconds. At 1 in the Modified Steps of Euler's Sieve,"Create set N of natural numbers from 1 to infinity." One cannot create the set of Natural numbers. If you honestly think you can, then take a sheet of paper and start writing all of the Natural numbers (seriously don't).

Secondly, what I said in general rules about your letter a in "The Proof".

Here is a paper you should be able to understand and is written correctly,"Groups as the Union of Subgroups".

Good advice except for the bolded. It is not uncommon to have sets with infinite members. Just because you can't physically write down every number in the set, doesn't mean that the set doesn't exist.

With standard set theory I can say something like "I have a set the contains all odd numbers and its cardinality is the same as a set containing all even numbers". That is a completely logical and true statement.

 

[Rudy Toody]

Thank you Estrella and Cogman.

In my next paper I will use: We start with the infinite set of all natural numbers > 0.

 

[Estrella]

Originally posted by: Cogman

Originally posted by: Estrella

Originally posted by: Rudy Toody

Originally posted by: Estrella
I know I am being a bit nit-picky but, what is it that you consider the literature? Is that all the Number Theory journals or something even more substantive?

I consider the literature to be everything published and available to the public.

Whatever I read, I chase the references to learn more. Then I chased those references.

For example: When I was a sophmore in high schooi, I decided to read every book ever written about parapsychology. I chased every book that was referenced by another book. I considered books that had no references to be of no value¹. By this process, I found every book. (In this case, I determined that there were too many circular references and not enough original research to convince me that parapsychology had any merit),

¹ Oops! I guess that submitting a math paper that has no references falls into that category.

Edit: Christopher Columbus used this method on the Flat Earth Conjecture.
Edit2: I just received Proofs from THE BOOK by Martin Aigner and Günter M. Ziegler, Second Edition

From the preface:

Paul Erdös liked to talk about The Book, is which God maintains the perfect proofs for mathematical theorems. following the dictum of G. H. Hardy that there is no permanant place for ugly mathematics.

The first chapter contains 6 proofs of the infinity of primes--from Euclid forward.

In my citations, could I cite this book as the source for a proof. Or, should I email Euclid to get a copy of his?

As I critique your paper I will assume you are right and I will only provide insight into how to write your paper.

Some General Rules:

1. In a scholarly math paper do not enumerate steps as you did in "Modified Steps of Euler's Sieve". Instead, you should use paragraphs which show clear logic. Every part of your argument should flow from what came before it.

2. Use notation SPARINGLY. Mathematical shorthand such as: for every, there exists, subset of whatever set, etc.; should be left on the blackboard or in your notebook.

3. Make sure your citations are at the end of the paper in a clearly marked section. You should cite by whatever the current MLA standards are.

4. Whenever you say by definition, it must be the actual definition. For instance you say,"By definition: There are infinite primes." There are not infinite primes by definition. There is a theorem which states such but, not a definition.

Yes, there are a lot of other rules too. I know I did not write nearly everything.

Now, I can tell you exactly why your paper was rejected in probably less than thirty seconds. At 1 in the Modified Steps of Euler's Sieve,"Create set N of natural numbers from 1 to infinity." One cannot create the set of Natural numbers. If you honestly think you can, then take a sheet of paper and start writing all of the Natural numbers (seriously don't).

Secondly, what I said in general rules about your letter a in "The Proof".

Here is a paper you should be able to understand and is written correctly,"Groups as the Union of Subgroups".

Good advice except for the bolded. It is not uncommon to have sets with infinite members. Just because you can't physically write down every number in the set, doesn't mean that the set doesn't exist.

With standard set theory I can say something like "I have a set the contains all odd numbers and its cardinality is the same as a set containing all even numbers". That is a completely logical and true statement.

My point is is that saying," Create N, the set of natural numbers" is equivalent to saying," Let x be in the set A." What if x doesn't want to be in A? It is not good use of language in a serious math paper. He should be stating things. Example: N is the set of Natural numbers, call this set PT(or Potential Twins). In actuality, the aforementioned is also silly. Example: A former teacher of mine was at a conference in which a very bright man who worked very hard started an argument with," Suppose a is in A, call this element x." The whole audience erupted in laughter.

I am not saying one cannot show a construction of a set with infinitely many terms. The way his paper is written, especially without a proper statement or a proper construction of the set explicitly written, made me think he was telling someone to write them down (since the word create is ambiguous in this sense). Create is a very handwavy term in mathematics. If I cannot write the set down element for element, then I better come up with a clever way of constructing ALL of those terms with minimal effort (whatever that means).

 

[Estrella]

Originally posted by: Rudy Toody
Thank you Estrella and Cogman.

In my next paper I will use: We start with the infinite set of all natural numbers > 0.

Unless you are part of the smaller camp(at least I think it is the smaller camp), every member of the set of natural numbers is more than zero. Secondly, saying N is infinite is incredibly redundant and will be greatly frowned upon.

 

[Cogman]

Originally posted by: Estrella

Originally posted by: Cogman

Originally posted by: Estrella

Originally posted by: Rudy Toody

Originally posted by: Estrella
I know I am being a bit nit-picky but, what is it that you consider the literature? Is that all the Number Theory journals or something even more substantive?

I consider the literature to be everything published and available to the public.

Whatever I read, I chase the references to learn more. Then I chased those references.

For example: When I was a sophmore in high schooi, I decided to read every book ever written about parapsychology. I chased every book that was referenced by another book. I considered books that had no references to be of no value¹. By this process, I found every book. (In this case, I determined that there were too many circular references and not enough original research to convince me that parapsychology had any merit),

¹ Oops! I guess that submitting a math paper that has no references falls into that category.

Edit: Christopher Columbus used this method on the Flat Earth Conjecture.
Edit2: I just received Proofs from THE BOOK by Martin Aigner and Günter M. Ziegler, Second Edition

From the preface:

Paul Erdös liked to talk about The Book, is which God maintains the perfect proofs for mathematical theorems. following the dictum of G. H. Hardy that there is no permanant place for ugly mathematics.

The first chapter contains 6 proofs of the infinity of primes--from Euclid forward.

In my citations, could I cite this book as the source for a proof. Or, should I email Euclid to get a copy of his?

As I critique your paper I will assume you are right and I will only provide insight into how to write your paper.

Some General Rules:

1. In a scholarly math paper do not enumerate steps as you did in "Modified Steps of Euler's Sieve". Instead, you should use paragraphs which show clear logic. Every part of your argument should flow from what came before it.

2. Use notation SPARINGLY. Mathematical shorthand such as: for every, there exists, subset of whatever set, etc.; should be left on the blackboard or in your notebook.

3. Make sure your citations are at the end of the paper in a clearly marked section. You should cite by whatever the current MLA standards are.

4. Whenever you say by definition, it must be the actual definition. For instance you say,"By definition: There are infinite primes." There are not infinite primes by definition. There is a theorem which states such but, not a definition.

Yes, there are a lot of other rules too. I know I did not write nearly everything.

Now, I can tell you exactly why your paper was rejected in probably less than thirty seconds. At 1 in the Modified Steps of Euler's Sieve,"Create set N of natural numbers from 1 to infinity." One cannot create the set of Natural numbers. If you honestly think you can, then take a sheet of paper and start writing all of the Natural numbers (seriously don't).

Secondly, what I said in general rules about your letter a in "The Proof".

Here is a paper you should be able to understand and is written correctly,"Groups as the Union of Subgroups".

Good advice except for the bolded. It is not uncommon to have sets with infinite members. Just because you can't physically write down every number in the set, doesn't mean that the set doesn't exist.

With standard set theory I can say something like "I have a set the contains all odd numbers and its cardinality is the same as a set containing all even numbers". That is a completely logical and true statement.

My point is is that saying," Create N, the set of natural numbers" is equivalent to saying," Let x be in the set A." What if x doesn't want to be in A? It is not good use of language in a serious math paper. He should be stating things. Example: N is the set of Natural numbers, call this set PT(or Potential Twins). In actuality, the aforementioned is also silly. Example: A former teacher of mine was at a conference in which a very bright man who worked very hard started an argument with," Suppose a is in A, call this element x." The whole audience erupted in laughter.

I am not saying one cannot show a construction of a set with infinitely many terms. The way his paper is written, especially without a proper statement or a proper construction of the set explicitly written, made me think he was telling someone to write them down (since the word create is ambiguous in this sense). Create is a very handwavy term in mathematics. If I cannot write the set down element for element, then I better come up with a clever way of constructing ALL of those terms with minimal effort (whatever that means).

Ahh, gotcha. Shows how many math papers I've written

 

[Rudy Toody]

Originally posted by: Estrella

Originally posted by: Rudy Toody
Thank you Estrella and Cogman.

In my next paper I will use: We start with the infinite set of all natural numbers > 0.

Unless you are part of the smaller camp(at least I think it is the smaller camp), every member of the set of natural numbers is more than zero. Secondly, saying N is infinite is incredibly redundant and will be greatly frowned upon.

How about the following for my next sieve?

The union of these four sets: NP (a set of one natural number-- the 1), NT (a set of the next two natural numbers),
PT(a set of the next four natural numbers), and PD (a set of the remaining natural numbers) equals the set of natural numbers.

 

[DrPizza]

Rudy, for the sake of simplicity, could you describe the original process in this thread in words, rather than with symbols for sets?
Thanks. I was going through it and trying to figure out your process, but I haven't the foggiest of what the set NP is.

It was pretty easy to understand the first part - potential twins
It's just two consecutive odd integers of which neither is divisible by 3. That twin primes (other than 2,3) would consist of two consecutive odd integers seems rather obvious.

So, we've got your set:
5,7;11,13;17,19;23,25;29,31;35,37;41,43;47,49;51,53;55,59;61,65;67,71;73,77;79,81;...

What's NP at this point? The empty set?

I went on. Step 2, selected the lowest prime (5) from both sets. (I guessed NP was the empty set at this point.)

Since it came from PT, 5 and 5+2 are twin primes. Got it.
Set C now becomes 7 and will be moved to NT in the next cycle..

Step 3. Multiply each number in N by 7?! Okay, 7, 14, 21, 28, 35, 42, 49,... This is temporary set P
Now, I do something else to create temporary set P? What did I just multiply each number by 7 for??
Huh?

Could you describe fully your process up to the number 100, perhaps??

 

[Rudy Toody]

NP is a set to hold the one. It is used only during the multiply. The union of the 4 sets is multiplied by the lowest prime. I have a set for the one so that in my arguments i can compare my sieve to Euler's Sieve. Otherwise, I will be one short of equal.

NT is the set of non-twins, which hold single primes and composites removed from set PT.

PT is like you said, pairs of odd numbers that might be twin primes.

PD is a new set for my new sieve. It will contain the rest of the natural number that have not been removed. PD stands for potential dual twins, such as 11,13,17,19 and 101,103,107,109. When a product matches this set, 4 items will be removed---the product, its matching twin number, and the matching possible twin prime. Example. when product is 49. the 49 is removed, 47 is moved to NT to be sieved there, and 41,43 are moved to PT to be sieved there. In this case, all three will be processed as primes, though that will not be the majority case. The majority will be all composites.

With this sieve, the twin primes will come out of PD and PT and the single primes will come out of NT.

The twins from PD will be the single twins--the ones that cannot be part of a dual twin prime.
The twins from PT will be the twins that were sent down from PD per the illustration above.

To make this a little clearer, I show the initial setup of the sets below:

NP = {1}
NT = {2,3}
TP = {4,5,6,7}
PD = {8,9,10,11,12,13,14,15, .....etc.}

Notice the powers of two for the start of each set.

TP is fed possible twins from PD
NT is fed possible primes from both PD and TP.

I think adding PD to the mix of sets will give me a better chance at proving that twin primes are infinite. The dual twins are probably infinite, but I don't think there will be enough information to prove this. I am going to look at Bertrand's postulate for ideas.

Anyway, sieving the 2 removes the even numbers from all the sets.
Sieving the 3 removes all multiples of 3 from the sets. At this point the union of the sets will be the same as in the first sieve.
Also at this point, set NT will be empty. This is new. For the selection process, this means that an empty set must be considered high to the lowest numbers of the other sets. Sieving the 5 will cause NT to be reloaded and it will never run out from that point on. (unless you are testing using a finite limit--then all sets will become empty, except NP).

Hope this helps a bit. I am not quite done with the analysis of the new sieve to tell you much more. I'll update this when I figure out a bit more.

 

[Rudy Toody]

To answer your last question: The seven is moved to NT by the remove function because when the 5 is removed, its partner the 7 is also removed. We only identified the twin and sieved its lower prime. Then we process the 7 out of NT, where we just put it, and remove all of its multiples (we create a new P for this step). The alternative to this method is to sieve both the 5 and 7 together. However, this makes the remove process a bit convoluted and I have chosen to let the remove process funtion the same in all situations.

 

[Rudy Toody]

I have got the new sieve working!

Below is all the dual twin primes below 100 000.

{{11,13},{17,19}}

{{101,103},{107,109}}

{{191,193},{197,199}}

{{821,823},{827,829}}

{{1481,1483},{1487,1489}}

{{1871,1873},{1877,1879}}

{{2081,2083},{2087,2089}}

{{3251,3253},{3257,3259}}

{{3461,3463},{3467,3469}}

{{5651,5653},{5657,5659}}

{{9431,9433},{9437,9439}}

{{13001,13003},{13007,13009}}

{{15641,15643},{15647,15649}}

{{15731,15733},{15737,15739}}

{{16061,16063},{16067,16069}}

{{18041,18043},{18047,18049}}

{{18911,18913},{18917,18919}}

{{19421,19423},{19427,19429}}

{{21011,21013},{21017,21019}}

{{22271,22273},{22277,22279}}

{{25301,25303},{25307,25309}}

{{31721,31723},{31727,31729}}

{{34841,34843},{34847,34849}}

{{43781,43783},{43787,43789}}

{{51341,51343},{51347,51349}}

{{55331,55333},{55337,55339}}

{{62981,62983},{62987,62989}}

{{67211,67213},{67217,67219}}

{{69491,69493},{69497,69499}}

{{72221,72223},{72227,72229}}

{{77261,77263},{77267,77269}}

{{79691,79693},{79697,79699}}

{{81041,81043},{81047,81049}}

{{82721,82723},{82727,82729}}

{{88811,88813},{88817,88819}}

{{97841,97843},{97847,97849}}

{{99131,99133},{99137,99139}}

 

[DrPizza]

Anyone else? I'm usually really good at following math textbooks. I can't make rhyme or reason out of his first sieve for double primes. I can't read step 6 either (I can barely make out "mod")

 

[Rudy Toody]

Originally posted by: DrPizza
Anyone else? I'm usually really good at following math textbooks. I can't make rhyme or reason out of his first sieve for double primes. I can't read step 6 either (I can barely make out "mod")

Here is a link to the new program code.

It should be easier to follow.