Sorry, an error occurred while loading the content.

• Hello all: Let F(n)=P(n)!-P(n)!!+2 P(n) n-th prime F(1)=2 Prime F(2)=5 Prime F(3)=107 Prime F(4)=4937 Prime Find another prime number in this secuence
Message 1 of 24 , Dec 18, 2002
View Source
• 0 Attachment
Hello all:

Let F(n)=P(n)!-P(n)!!+2

P(n) n-th prime

F(1)=2 Prime
F(2)=5 Prime
F(3)=107 Prime
F(4)=4937 Prime

Find another prime number in this secuence

Sincerely

Sebastián Martín Ruiz
www.telefonica.net/c/smruiz

___________________________________________________
Yahoo! Sorteos
Consulta si tu número ha sido premiado en
Yahoo! Sorteos http://loteria.yahoo.es
• Hi All, Factorials and Multifactorials being my interest I couldn t resist having a go at this The answer is F(262)= 1667!-1667!!+2 Now I could just leave it
Message 2 of 24 , Dec 18, 2002
View Source
• 0 Attachment
Hi All,
Factorials and Multifactorials being my interest I couldn't resist
having a go at this
The answer is F(262)= 1667!-1667!!+2
Now I could just leave it at that but my inate honesty forces me to
admit that though I have very strong evidence as follows
(1667!)-(1667!2)+2 is 2-PRP! (18.036000 seconds)
(1667!)-(1667!2)+2 is 3-PRP! (18.046000 seconds)
(1667!)-(1667!2)+2 is 5-PRP! (18.817000 seconds)
(1667!)-(1667!2)+2 is 7-PRP! (18.096000 seconds)
(1667!)-(1667!2)+2 is 11-PRP! (18.036000 seconds)
(1667!)-(1667!2)+2 is 13-PRP! (18.026000 seconds)
(1667!)-(1667!2)+2 is 17-PRP! (19.709000 seconds)
(1667!)-(1667!2)+2 is 19-PRP! (18.236000 seconds)
(1667!)-(1667!2)+2 is 23-PRP! (18.216000 seconds)
(1667!)-(1667!2)+2 is 29-PRP! (19.669000 seconds)
(1667!)-(1667!2)+2 is 31-PRP! (18.867000 seconds)
i.e. it is prp in 11 (another number I have a strong interest in)
bases
and
Primality testing (1667!)-(1667!2)+2 [N-1/N+1, Brillhart-Lehmer-
Selfridge]
Calling N+1 BLS with factored part 0.12% and helper 0.01% (0.39%
proof)
(1667!)-(1667!2)+2 is Fermat and Lucas PRP! (86.504000 seconds)

Now while the above may be good enough for government work it doesn't
constitute a proof.
As yet I have only been iterested (and proven)primes that are +/-1
which means as I get
(1667!)-(1667!2)+1 has factors: 2*4682677
cofactor has no small factor.
and
(1667!)-(1667!2)+3 has factors: 2^7*3*2293
cofactor has no small factor.
I don't have the tools to prove this number prime.
However as it only contains 4650 digits It should be provable.
Could someone point me in the direction of an appropriate program
that
I could download and use to verify F(262) primeness.

As an aside I have never seen a prp that involves factorials that is
not prime.
I offer the conjecture that "being prp sufficient to prove the
primality of factorials and multifactorials"
Cheers
Ken
--- In primenumbers@yahoogroups.com, Sebastian Martin
<sebi_sebi@y...> wrote:
> Hello all:
>
> Let F(n)=P(n)!-P(n)!!+2
>
> P(n) n-th prime
>
>
> F(1)=2 Prime
> F(2)=5 Prime
> F(3)=107 Prime
> F(4)=4937 Prime
>
> Find another prime number in this secuence
>
> Sincerely
>
> Sebastián Martín Ruiz
> www.telefonica.net/c/smruiz
>
> ___________________________________________________
> Yahoo! Sorteos
> Consulta si tu número ha sido premiado en
> Yahoo! Sorteos http://loteria.yahoo.es
• Ken: http://www.znz.freesurf.fr/files/po200b3.zip will get you there in a couple of GHz-months; David
Message 3 of 24 , Dec 18, 2002
View Source
• 0 Attachment
Ken:
http://www.znz.freesurf.fr/files/po200b3.zip
will get you there in a couple of GHz-months;
David
• ... is ... Does 5!-7!3-1 = 91 = 7*13 is 3-PRP meet your criteria? Paul
Message 4 of 24 , Dec 18, 2002
View Source
• 0 Attachment
> Ken Davis wrote:
> As an aside I have never seen a prp that involves factorials that
is
> not prime.
> I offer the conjecture that "being prp sufficient to prove the
> primality of factorials and multifactorials"

Does 5!-7!3-1 = 91 = 7*13 is 3-PRP meet your criteria?

Paul
• Hi Paul, ... No. Sorry for not being clear. I meant Strict factorials or multifactorials. And I also don t mean cases that allow slight of hand through the
Message 5 of 24 , Dec 18, 2002
View Source
• 0 Attachment
Hi Paul,
> Does 5!-7!3-1 = 91 = 7*13 is 3-PRP meet your criteria?
No.
Sorry for not being clear.
I meant Strict factorials or multifactorials.
And I also don't mean cases that allow slight of hand through the
definition of a multifactorial (eg 561!562)
So to put my conjecture on a more mathematical footing
For n,m integer
m >= 1
n>m
if n!m+1 is prp in any base then it is prime.
if n!m-1 is prp in any base then it is prime.
Cheers
Ken
--- In primenumbers@yahoogroups.com, "paulunderwooduk
<paulunderwood@m...>" <paulunderwood@m...> wrote:
> > Ken Davis wrote:
> > As an aside I have never seen a prp that involves factorials that
> is
> > not prime.
> > I offer the conjecture that "being prp sufficient to prove the
> > primality of factorials and multifactorials"
>
> Does 5!-7!3-1 = 91 = 7*13 is 3-PRP meet your criteria?
>
> Paul
• ... The first Carmichael number 561=3*11*17 is 2-PRP but this equals 260! 258+1 = 130!126+1 = 65!57+1 Paul
Message 6 of 24 , Dec 18, 2002
View Source
• 0 Attachment
> > Does 5!-7!3-1 = 91 = 7*13 is 3-PRP meet your criteria?
> No.
> Sorry for not being clear.
> I meant Strict factorials or multifactorials.
> And I also don't mean cases that allow slight of hand through the
> definition of a multifactorial (eg 561!562)
> So to put my conjecture on a more mathematical footing
> For n,m integer
> m >= 1
> n>m
> if n!m+1 is prp in any base then it is prime.
> if n!m-1 is prp in any base then it is prime.
> Cheers
> Ken

The first Carmichael number 561=3*11*17 is 2-PRP but this equals 260!
258+1 = 130!126+1 = 65!57+1

Paul
• oops I can t divide by two! ... 260! ... Oops! That should be 561 = 280!278+1 = 140!136 = 70!62 Paul
Message 7 of 24 , Dec 18, 2002
View Source
• 0 Attachment
oops I can't divide by two!
> > > Does 5!-7!3-1 = 91 = 7*13 is 3-PRP meet your criteria?
> > No.
> > Sorry for not being clear.
> > I meant Strict factorials or multifactorials.
> > And I also don't mean cases that allow slight of hand through the
> > definition of a multifactorial (eg 561!562)
> > So to put my conjecture on a more mathematical footing
> > For n,m integer
> > m >= 1
> > n>m
> > if n!m+1 is prp in any base then it is prime.
> > if n!m-1 is prp in any base then it is prime.
> > Cheers
> > Ken
>
> The first Carmichael number 561=3*11*17 is 2-PRP but this equals
260!
> 258+1 = 130!126+1 = 65!57+1
>

Oops! That should be 561 = 280!278+1 = 140!136 = 70!62

Paul
• Well done Paul, That certainly dissproves my conjecture. I was thinking about it over lunch and was not surprised to find your reply. But I still think there
Message 8 of 24 , Dec 18, 2002
View Source
• 0 Attachment
Well done Paul,
That certainly dissproves my conjecture.
I was thinking about it over lunch and was not surprised to find your
But I still think there is something to it, I just have to make
a "weasel move" and change my conjecture to avoid your clever
solution.
It seems to me it relies on the multifactorial consisting of only 2
numbers.
Remember I'm a beginner at this so having had 2 strikes here's my
third swing at it.
For n,m integer
m >= 1
n/2>m (this is to ensure that the multifactorial has at least 3
multipliers)
if n!m+1 is prp in any base then it is prime.
if n!m-1 is prp in any base then it is prime.

If this is to vague to qualify as a conjecture I think dispproving it
would be equivalen to the following puzzle.
Find a prp (which is not prime) which is +/-1 from a number that can
be expressed as a multiple of an AP (of length >=3).
so
560= 2^4*5*7 and 562= 2*281 won't work
Cheers
Ken
--- In primenumbers@yahoogroups.com, "paulunderwooduk
<paulunderwood@m...>" <paulunderwood@m...> wrote:
> oops I can't divide by two!
> > > > Does 5!-7!3-1 = 91 = 7*13 is 3-PRP meet your criteria?
> > > No.
> > > Sorry for not being clear.
> > > I meant Strict factorials or multifactorials.
> > > And I also don't mean cases that allow slight of hand through
the
> > > definition of a multifactorial (eg 561!562)
> > > So to put my conjecture on a more mathematical footing
> > > For n,m integer
> > > m >= 1
> > > n>m
> > > if n!m+1 is prp in any base then it is prime.
> > > if n!m-1 is prp in any base then it is prime.
> > > Cheers
> > > Ken
> >
> > The first Carmichael number 561=3*11*17 is 2-PRP but this equals
> 260!
> > 258+1 = 130!126+1 = 65!57+1
> >
>
> Oops! That should be 561 = 280!278+1 = 140!136 = 70!62
>
> Paul
• ... Three strikes: you re out! 10!4+1 = 10*6*2+1 = 121 is 7-PRP Paul
Message 9 of 24 , Dec 18, 2002
View Source
• 0 Attachment
> Remember I'm a beginner at this so having had 2 strikes here's my
> third swing at it.
> For n,m integer
> m >= 1
> n/2>m (this is to ensure that the multifactorial has at least 3
> multipliers)
> if n!m+1 is prp in any base then it is prime.
> if n!m-1 is prp in any base then it is prime.
>
Three strikes: you're out!

10!4+1 = 10*6*2+1 = 121 is 7-PRP

Paul
• ... Correction: its 3-PRP source: http://primes.utm.edu/glossary/page.php?sort=PRP Paul
Message 10 of 24 , Dec 18, 2002
View Source
• 0 Attachment
> 10!4+1 = 10*6*2+1 = 121 is 7-PRP

Correction: its 3-PRP

source:

http://primes.utm.edu/glossary/page.php?sort=PRP

Paul
• Well Done. That convinces even me. Oh well I suppose I ll have to continue proving the multifactorial prp s I find are prime. Cheers Ken
Message 11 of 24 , Dec 18, 2002
View Source
• 0 Attachment
Well Done.
That convinces even me.
Oh well I suppose I'll have to continue proving the multifactorial
prp's I find are prime.
Cheers
Ken
--- In primenumbers@yahoogroups.com, "paulunderwooduk
<paulunderwood@m...>" <paulunderwood@m...> wrote:
> > 10!4+1 = 10*6*2+1 = 121 is 7-PRP
>
> Correction: its 3-PRP
>
> source:
>
> http://primes.utm.edu/glossary/page.php?sort=PRP
>
> Paul
• Ken: These will fool you in any base: 550*1566*2582+1 is 137-PRP! 864*1412*1960+1 is 137-PRP! 186*2585*4984+1 is 137-PRP! 225*2496*4767+1 is 137-PRP!
Message 12 of 24 , Dec 18, 2002
View Source
• 0 Attachment
Ken: These will fool you in any base:

550*1566*2582+1 is 137-PRP!
864*1412*1960+1 is 137-PRP!
186*2585*4984+1 is 137-PRP!
225*2496*4767+1 is 137-PRP!
696*1580*2464+1 is 137-PRP!
693*1744*2795+1 is 137-PRP!
790*1715*2640+1 is 137-PRP!
216*3020*5824+1 is 137-PRP!
704*1848*2992+1 is 137-PRP!
584*2002*3420+1 is 137-PRP!
126*4015*7904+1 is 137-PRP!
76*5148*10220+1 is 137-PRP!
284*3058*5832+1 is 137-PRP!
472*2522*4572+1 is 137-PRP!
• Moreover, 36*41*46*51*56+1 is a Carmichael number.
Message 13 of 24 , Dec 19, 2002
View Source
• 0 Attachment
Moreover, 36*41*46*51*56+1 is a Carmichael number.
• A prime puzzle, I have 6 numbers: 1,2,3 22,25 and 1111 find a primeformula using these numbers (hint: divide 1111 into 2x11).. success! RJ
Message 14 of 24 , Apr 4, 2005
View Source
• 0 Attachment
A prime puzzle,

I have 6 numbers: 1,2,3 22,25 and 1111

find a primeformula using these numbers (hint: divide 1111 into 2x11)..

success!

RJ
• What is this sequence ? 57,46,41,42,49,62,81,106,137,...
Message 15 of 24 , Dec 9, 2011
View Source
• 0 Attachment
What is this sequence ?

57,46,41,42,49,62,81,106,137,...
• It has g.f. (74 x^2 - 125 x + 57)/(x - 1)^3 and goes on: 57, 46, 41, 42, 49, 62, 81, 106, 137, 174, 217, 266, 321, 382, 449, 522, 601, 686, 777, 874, 977,
Message 16 of 24 , Dec 9, 2011
View Source
• 0 Attachment
It has g.f. (74 x^2 - 125 x + 57)/(x - 1)^3
and goes on:
57, 46, 41, 42, 49, 62, 81, 106, 137, 174, 217, 266, 321, 382, 449,
522, 601, 686, 777, 874, 977, 1086, 1201, 1322, 1449, 1582, 1721,
1866, 2017, 2174, 2337, 2506, 2681, 2862, 3049, 3242, 3441, 3646,
3857, 4074, 4297, 4526, 4761, 5002, 5249, 5502, 5761, 6026, 6297,
6574, 6857, 7146, 7441, 7742, 8049, 8362, 8681, 9006, 9337, 9674,
10017, 10366, 10721, 11082, 11449, 11822, 12201, 12586, 12977, 13374,
13777, 14186, 14601, 15022, 15449, 15882, 16321, 16766, 17217, 17674,
18137, 18606, 19081, 19562, 20049, 20542, 21041,

Maximilian

On Fri, Dec 9, 2011 at 12:16 PM, ajo <sopadeajo2001@...> wrote:
> What is this sequence ?
>
> 57,46,41,42,49,62,81,106,137,...
>
>
>
> ------------------------------------
>
> Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
> The Prime Pages : http://www.primepages.org/
>
> Yahoo! Groups Links
>
>
>
• I haven t comprehended Maximilian s result but 3x^2 - 14x + 57 works. Mark
Message 17 of 24 , Dec 9, 2011
View Source
• 0 Attachment
I haven't comprehended Maximilian's result but
3x^2 - 14x + 57
works.

Mark

--- In primenumbers@yahoogroups.com, Maximilian Hasler <maximilian.hasler@...> wrote:
>
> It has g.f. (74 x^2 - 125 x + 57)/(x - 1)^3
> and goes on:
> 57, 46, 41, 42, 49, 62, 81, 106, 137, 174, 217, 266, 321, 382, 449,
> 522, 601, 686, 777, 874, 977, 1086, 1201, 1322, 1449, 1582, 1721,
> 1866, 2017, 2174, 2337, 2506, 2681, 2862, 3049, 3242, 3441, 3646,
> 3857, 4074, 4297, 4526, 4761, 5002, 5249, 5502, 5761, 6026, 6297,
> 6574, 6857, 7146, 7441, 7742, 8049, 8362, 8681, 9006, 9337, 9674,
> 10017, 10366, 10721, 11082, 11449, 11822, 12201, 12586, 12977, 13374,
> 13777, 14186, 14601, 15022, 15449, 15882, 16321, 16766, 17217, 17674,
> 18137, 18606, 19081, 19562, 20049, 20542, 21041,
>
> Maximilian
>
>
>
> On Fri, Dec 9, 2011 at 12:16 PM, ajo <sopadeajo2001@...> wrote:
> > What is this sequence ?
> >
> > 57,46,41,42,49,62,81,106,137,...
> >
> >
> >
> > ------------------------------------
> >
> > Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
> > The Prime Pages : http://www.primepages.org/
> >
> > Yahoo! Groups Links
> >
> >
> >
>
• Oops, sorry, there was an error of sign in the denominator. It should be gf = (74 x^2 - 125 x + 57)/(1 - x)^3 = 57 + 46*x + 41*x^2 + 42*x^3 + 49*x^4 + 62*x^5 +
Message 18 of 24 , Dec 9, 2011
View Source
• 0 Attachment
Oops, sorry, there was an error of sign in the denominator.
It should be
gf = (74 x^2 - 125 x + 57)/(1 - x)^3
= 57 + 46*x + 41*x^2 + 42*x^3 + 49*x^4 + 62*x^5 + 81*x^6 + 106*x^7
+ 137*x^8 + 174*x^9 + 217*x^10 + 266*x^11 + 321*x^12 + 382*x^13
+ 449*x^14 + 522*x^15 + 601*x^16 + 686*x^17 + 777*x^18 + O(x^19)

Maximilian

On Fri, Dec 9, 2011 at 12:45 PM, Mark <mark.underwood@...> wrote:
>
> I haven't comprehended Maximilian's result but
> 3x^2 - 14x + 57
> works.
>
> Mark
>
>
> --- In primenumbers@yahoogroups.com, Maximilian Hasler <maximilian.hasler@...> wrote:
>>
>> It has g.f. (74 x^2 - 125 x + 57)/(x - 1)^3
>> and goes on:
>> 57, 46, 41, 42, 49, 62, 81, 106, 137, 174, 217, 266, 321, 382, 449,
>> 522, 601, 686, 777, 874, 977, 1086, 1201, 1322, 1449, 1582, 1721,
>> 1866, 2017, 2174, 2337, 2506, 2681, 2862, 3049, 3242, 3441, 3646,
>> 3857, 4074, 4297, 4526, 4761, 5002, 5249, 5502, 5761, 6026, 6297,
>> 6574, 6857, 7146, 7441, 7742, 8049, 8362, 8681, 9006, 9337, 9674,
>> 10017, 10366, 10721, 11082, 11449, 11822, 12201, 12586, 12977, 13374,
>> 13777, 14186, 14601, 15022, 15449, 15882, 16321, 16766, 17217, 17674,
>> 18137, 18606, 19081, 19562, 20049, 20542, 21041,
>>
>> Maximilian
>>
>>
>>
>> On Fri, Dec 9, 2011 at 12:16 PM, ajo <sopadeajo2001@...> wrote:
>> > What is this sequence ?
>> >
>> > 57,46,41,42,49,62,81,106,137,...
>> >
>> >
>> >
>> > ------------------------------------
>> >
>> > Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
>> > The Prime Pages : http://www.primepages.org/
>> >
>> > Yahoo! Groups Links
>> >
>> >
>> >
>>
>
>
>
>
> ------------------------------------
>
> Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
> The Prime Pages : http://www.primepages.org/
>
> Yahoo! Groups Links
>
>
>
• ... It looks like it s just the quadratic 3*x^2-20*x+74.
Message 19 of 24 , Dec 9, 2011
View Source
• 0 Attachment
> ? vector(9,x,3*x^2-20*x+74)
> [57, 46, 41, 42, 49, 62, 81, 106, 137]

It looks like it's just the quadratic 3*x^2-20*x+74.

On 12/9/2011 8:40 AM, Maximilian Hasler wrote:
> It has g.f. (74 x^2 - 125 x + 57)/(x - 1)^3
> and goes on:
> 57, 46, 41, 42, 49, 62, 81, 106, 137, 174, 217, 266, 321, 382, 449,
> 522, 601, 686, 777, 874, 977, 1086, 1201, 1322, 1449, 1582, 1721,
> 1866, 2017, 2174, 2337, 2506, 2681, 2862, 3049, 3242, 3441, 3646,
> 3857, 4074, 4297, 4526, 4761, 5002, 5249, 5502, 5761, 6026, 6297,
> 6574, 6857, 7146, 7441, 7742, 8049, 8362, 8681, 9006, 9337, 9674,
> 10017, 10366, 10721, 11082, 11449, 11822, 12201, 12586, 12977, 13374,
> 13777, 14186, 14601, 15022, 15449, 15882, 16321, 16766, 17217, 17674,
> 18137, 18606, 19081, 19562, 20049, 20542, 21041,
>
> Maximilian
>
>
>
> On Fri, Dec 9, 2011 at 12:16 PM, ajo<sopadeajo2001@...> wrote:
>> What is this sequence ?
>>
>> 57,46,41,42,49,62,81,106,137,...
>>
>>
>>
>> ------------------------------------
>>
>> Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
>> The Prime Pages : http://www.primepages.org/
>>
>> Yahoo! Groups Links
>>
>>
>>
>
>
> ------------------------------------
>
> Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
> The Prime Pages : http://www.primepages.org/
>
> Yahoo! Groups Links
>
>
>
>
>
• ... I agree - the two sequences coincide. And I admit that the quadratic is a simpler description, but since I had my ggf() at hand, I found the other before.
Message 20 of 24 , Dec 9, 2011
View Source
• 0 Attachment
On Fri, Dec 9, 2011 at 12:56 PM, Jack Brennen <jfb@...> wrote:
>
>> ? vector(9,x,3*x^2-20*x+74)
>> [57, 46, 41, 42, 49, 62, 81, 106, 137]
>
>
> It looks like it's just the quadratic 3*x^2-20*x+74.

I agree - the two sequences coincide.
And I admit that the quadratic is a simpler description,
but since I had my ggf() at hand, I found the other before.

Maximilian
• The values you give seem to be correct, but the polynomials wrong: ? for(x=2,20, print(f(x))) 103 87/2 247/9 641/32 1971/125 13 3793/343 2463/256 2069/243
Message 21 of 24 , Dec 9, 2011
View Source
• 0 Attachment
The values you give seem to be correct, but the polynomials wrong:

? for(x=2,20, print(f(x)))
103
87/2
247/9
641/32
1971/125
13
3793/343
2463/256
2069/243
1909/250
9213/1331
1823/288
12811/2197
1854/343
1889/375
9659/2048
21783/4913
2033/486
27157/6859

[Non-text portions of this message have been removed]
• Ok, but now can anybody tell where the idea came from ,or in other words, what do these numbers originally pretend to represent ? [Non-text portions of this
Message 22 of 24 , Dec 9, 2011
View Source
• 0 Attachment
Ok, but now can anybody tell where the idea came from ,or in other words, what do these numbers originally pretend to represent ?

[Non-text portions of this message have been removed]
• ... The worst case scenario is that the original number sequence came from someone s high school homework assignment. :)
Message 23 of 24 , Dec 9, 2011
View Source
• 0 Attachment
--- In primenumbers@yahoogroups.com, Robin Garcia <sopadeajo2001@...> wrote:
>
> Ok, but now can anybody tell where the idea came from ,or in other words, what do these numbers originally pretend to represent ?
>
> [Non-text portions of this message have been removed]
>

The worst case scenario is that the original number sequence came from someone's high school homework assignment. :)
• The worst case scenario is that the original number sequence came from someone s high school homework assignment. :) Well, yes the level is not a high level.
Message 24 of 24 , Dec 9, 2011
View Source
• 0 Attachment
"The worst case scenario is that the original number sequence came from someone's high school homework assignment. :)"

Well, yes the level is not a high level. What i mean is the polinomial fits  pretty well, but originally i was thinking
in a base b and numbers  b^2+(b-2^2)^2+(b-3^2)^2.  Nothing very hard, but for b=10 you get 10^2+6^2+1^2=137,
which obsesses so much David.  It was just fun for me.

[Non-text portions of this message have been removed]
Your message has been successfully submitted and would be delivered to recipients shortly.