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 2015-10-30, 22:07 #1 rogue     "Mark" Apr 2003 Between here and the 643210 Posts Smarandache-Wellin Primes I've been working on a change to pfgw to support searching for prime Smarandache-Wellin numbers. Although similar to Smarandache numbers, these differ because the sequence only includes prime numbers. Think of it this way, Smarandache is to factorials and Smarandache-Wellin is to primorials. The new expressions are SmW and SmWp (along with the reverse forms of SmW_r and SmWp_r). SmW(11) (and SmW(12)) is equivalent to 235711 which SmWp(5) = 235711. I am also working on a sieve, but I need to dig up my old psieve code used for the primorial search. I suspect that Serge's sieve for Smarandache could quickly be modified to support this form. Last fiddled with by rogue on 2016-06-14 at 20:45
2015-10-30, 22:50   #2
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

957110 Posts

Quote:
 Originally Posted by rogue I suspect that Serge's sieve for Smarandache could quickly be modified to support this form.
It will be not exactly the same, because Smarandache sieve has an implicit summation built in. Can't think of a generalization of Sm-W() sum of weighted powers of 10.

...Unrelatedly, just recently I was browsing the web and did away with my misconception that Smarandache would be either a rather old person or a late classic from, say, 19th century. But no! He is a 'regular guy' of our age! What a pleasant surprise!
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2015-10-30, 23:09   #3
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

20C016 Posts

Quote:
 Originally Posted by rogue I am also working on a sieve, but I need to dig up my old psieve code used for the primorial search. I suspect that Serge's sieve for Smarandache could quickly be modified to support this form.
one thing I'd note is any time that the number of 1 mod 6 primes is one higher than the 5 mod 6 primes the number produced divides by 3. sadly I don't think that's regular enough to help much. edit:doh I realized there's other conditions that it happens for any time 5 mod 6 primes are 2 mod 3 ahead and any time 1 mod 6 are 1 mod 3 ahead technically as that's when the mod by 3 works out for the number made.

Last fiddled with by science_man_88 on 2015-10-31 at 00:00

2015-10-31, 04:03   #4
LaurV
Romulan Interpreter

"name field"
Jun 2011
Thailand

263B16 Posts

Quote:
 Originally Posted by Batalov ...Unrelatedly, just recently I was browsing the web and did away with my misconception that Smarandache would be either a rather old person or a late classic from, say, 19th century. But no! He is a 'regular guy' of our age! What a pleasant surprise!
Yes, we knew about him for long time, but we don't know him personally, he is born in the diameterally-opposite part of the country.

The name itself (pronounced "smah-run-dah-ke" with ke as in chemistry, and not with English ch sound as in check) is a very specific Romanian name, quite common over the part of the country where he was born. Sometime is found in Jewish or Greek communities too. It is specific in the sense that the root of the name came from an old Latin word smaragdus taken from old Greek sbaragdus, in turn coming from old Jewish barraktu meaning "shiny stone". From that, Romanian made smarand, Spanish made esmeralda (also a common girl name), and English made emerald (losing letters as it is going far away from the source ) and only Romanians transformed L/G into N (quite common for other Latin words too! we insert N in many places where it should not be).

It was a common practice before the 20th century to give to a girl with green eyes the name Smaranda (you can google the name to see many personalities having this name around the world, they are all Romanian, or with Romanian roots) and Smarandache, just meant "son of Smaranda", at the time when everybody has to have a family name, and this was transformed into a family name. In the modern (literary) speaking, the smarand was also transformed into (or back to) smarald (which is more difficult to pronounce, due to L-D alliteration, in Romanian we pronounce as we write, each letter makes a sound, and only this sound, no matter the word, Spanish solved that by adding the "a" which makes L and D to be part of different syllables), but the names stayed with n (easier to pronounce). The name is recognizable as being a Romanian name, by any Romanian, any time, anywhere in the world.

You should wonder if there might be a reason why we jumped in when we saw the topic title, from the very beginning of this the other thread... [edit, first we didn't see this is a different thread]

Last fiddled with by LaurV on 2015-10-31 at 04:19 Reason: small additions, grammar, grammar, grammar...

 2015-11-03, 17:38 #5 rogue     "Mark" Apr 2003 Between here and the 144408 Posts I am trying to modify fpsieve to support sieving for this form, but I will need some help from someone who knows 64-bit x86 assembly.
 2015-11-03, 23:33 #6 rogue     "Mark" Apr 2003 Between here and the 25×3×67 Posts I tried this mod but got a segmentation fault: Code:  imul %rax, %rbp imul %rax, %rbx imul %rax, %rcx imul %rax, %rdx cmp %eax, 10 jge fmae2 mov %edi, 10 jmp fma fmae2: cmp %eax, 100 jge fmae3 mov %edi, 100 jmp fma fmae3: cmp %eax, 1000 jge fmae4 mov %edi, 1000 jmp fma fmae4: cmp %eax, 10000 jge fmae5 mov %edi, 10000 jmp fma fmae5: cmp %eax, 100000 jge fmae6 mov %edi, 100000 jmp fma fmae6: cmp %eax, 1000000 jge fmaen mov %edi, 1000000 jmp fma fmaen: mov %edi, 10000000 fma: cvtsi2sd %edi, %xmm9 VFMADD132SD %xmm1, %xmm0, %xmm9 VFMADD132SD %xmm2, %xmm0, %xmm9 VFMADD132SD %xmm3, %xmm0, %xmm9 VFMADD132SD %xmm4, %xmm0, %xmm9 mulsd %xmm5, %xmm1 mulsd %xmm6, %xmm2 mulsd %xmm7, %xmm3 mulsd %xmm8, %xmm4 This mod was made to primorial4_x64_64.S. Can someone tell me what is wrong with it? Better yet, can someone write asm code that will do what I need it to for this search?
2015-11-04, 06:21   #7
Antonio

"Antonio Key"
Sep 2011
UK

53110 Posts

Quote:
 Originally Posted by rogue I've been working on a change to pfgw to support searching for prime Smarandache-Wellin numbers. Although similar to Smarandache numbers, these differ because the sequence only includes prime numbers. Think of it this way, Smarandache is to factorials and Smarandache-Wellin is to primordials. The new expressions are SmW and SmWp (along with the reverse forms of SmW_r and SmWp_r). SmW(11) (and SmW(12)) is equivalent to 235711 which SmWp(5) = 235711. I am also working on a sieve, but I need to dig up my old psieve code used for the primorial search. I suspect that Serge's sieve for Smarandache could quickly be modified to support this form.
How do you define SmW_r and SmWp_r such that they are worth searching for primes?

2015-11-04, 13:35   #8
rogue

"Mark"
Apr 2003
Between here and the

144408 Posts

Quote:
 Originally Posted by Antonio How do you define SmW_r and SmWp_r such that they are worth searching for primes?
It is the reverse concatenation of primes just as Sm_r is the reverse concatenation of integers.

2015-11-04, 14:05   #9
axn

Jun 2003

19×271 Posts

Quote:
 Originally Posted by rogue It is the reverse concatenation of primes just as Sm_r is the reverse concatenation of integers.
... ending in 2 and thus all of them are even (is the point he was trying to make).

2015-11-04, 15:13   #10
rogue

"Mark"
Apr 2003
Between here and the

25·3·67 Posts

Quote:
 Originally Posted by axn ... ending in 2 and thus all of them are even (is the point he was trying to make).
D'oh!

2015-11-04, 18:19   #11
Antonio

"Antonio Key"
Sep 2011
UK

32·59 Posts

Quote:
 Originally Posted by rogue D'oh!
I think I saw a penny drop (and being the miserly sort, I'm searching the floor as I type)

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