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.

[QUOTE=rogue;414353]I suspect that Serge's sieve for Smarandache could quickly be modified to support this form.[/QUOTE]
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 '[URL="http://math.wikia.com/wiki/Florentin_Smarandache"]regular guy[/URL]' of our age! What a pleasant surprise!

[QUOTE=rogue;414353]

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.[/QUOTE]

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.

[QUOTE=Batalov;414355]...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 '[URL="http://math.wikia.com/wiki/Florentin_Smarandache"]regular guy[/URL]' of our age! What a pleasant surprise![/QUOTE]
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 [I]ke[/I] as in[I] chemistry[/I], and [U]not[/U] with English [I]ch[/I] sound as in [I]check[/I]) 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 [I]smaragdus[/I] taken from old Greek [I]sbaragdus[/I], in turn coming from old Jewish [I]barraktu[/I] meaning "shiny stone". From that, Romanian made [I]smarand[/I], Spanish made [I]esmeralda[/I] (also a common girl name), and English made [I]emerald[/I] (losing letters as it is going far away from the source :smile:) 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 [I]smarand[/I] was also transformed into (or back to) [I]smarald[/I] (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 [I]n[/I] (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 [STRIKE]this [/STRIKE] the other thread... :razz: [edit, first we didn't see this is a different thread]

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.

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
[/code]

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?

[QUOTE=rogue;414353]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.[/QUOTE]

How do you define SmW_r and SmWp_r such that they are worth searching for primes?

[QUOTE=Antonio;414917]How do you define SmW_r and SmWp_r such that they are worth searching for primes?[/QUOTE]

It is the reverse concatenation of primes just as Sm_r is the reverse concatenation of integers.

[QUOTE=rogue;414938]It is the reverse concatenation of primes just as Sm_r is the reverse concatenation of integers.[/QUOTE]

... ending in 2 and thus all of them are even (is the point he was trying to make).

[QUOTE=axn;414943]... ending in 2 and thus all of them are even (is the point he was trying to make).[/QUOTE]

D'oh!

[QUOTE=rogue;414946]D'oh![/QUOTE]

I think I saw a penny drop :smile: (and being the miserly sort, I'm searching the floor as I type)