20151109, 20:32  #144  
"Rashid Naimi"
Oct 2015
Remote to Here/There
2×7×139 Posts 
Quote:
I understand your pointers. The few k digit primes started as a means of putting into practice the concept of generating primes using my theorems and evolved into a hobby of bettering my personal bests till I would reach the limitation of the free WDP account. It was not meant to break any other records. PrimeQ was used because I did not know it was just a probability test. NextPrime would not serve any purpose for me. it would be the same as a random prime generation. At this point my prime 2Do list is to: Add to the WDP code that I have written, the codes necessary to generate an automatic mathematical expression of the number. Try to come up with the math for the sum in Theorem 2 to converge to less than the square of the largest factor in general or in particularly large (Billion+ digits). Failing that to submit it for publication, knowing well that it may be refused. 

20151109, 20:36  #145  
"Rashid Naimi"
Oct 2015
Remote to Here/There
2×7×139 Posts 
Quote:
Last fiddled with by a1call on 20151109 at 20:38 

20151109, 22:28  #146  
"Rashid Naimi"
Oct 2015
Remote to Here/There
2·7·139 Posts 
Quote:
Thank you for editing the title. It bothered me too. The correct and auto generated mathematical expression for the 5121 digit prime(?) number is: (61#1 +42 x 61#)!^{(61#)} + 61# x 49 The code to generate the expression as well as the number on the WDP is Code:
fctrlcntmns1=42; primorialBase=61; bsenmbersbtrctr=1; cntrbase=1; prmrlpwr=Prime[primorialBase]; Print ["Largest prime = ",Text[Style[prmrlpwr, Bold,FontSize > 13,Blue]]] prmrl=1; Do[prmrl=prmrl*Prime[n], {n, primorialBase}] Print["Primorial=",Text[Style[prmrl, Bold,FontSize > 13,Blue]]]; bsenmbr=prmrlbsenmbersbtrctr; Print["Base Number ",Text[Style[bsenmbr, Bold,FontSize > 13,Blue]]," is Prime= ",Text[Style[PrimeQ[bsenmbr], Bold,FontSize > 13,Blue]]] fctrl=bsenmbr; Do[fctrl=fctrl*(bsenmbr+(prmrl*n)), {n, fctrlcntmns1}] prmcnddte=fctrlprmrl*prmrlpwr; multiplier=1; Catch[Do[ prmcnddte=fctrl+prmrl*l; multiplier=l; ; If[PrimeQ[prmcnddte], Throw[prmcnddte]] ,{l,cntrbase,prmrlpwr}]] Print ["Candidate is prime is ",Text[Style[PrimeQ[prmcnddte], Bold,FontSize > 23,Blue]]," ",Text[Style[prmcnddte, Bold,FontSize > 13,Blue]]] Print["integer length=",Text[Style[IntegerLength[prmcnddte], Bold,FontSize > 19,Blue]]] Print["Mathematical Expression = (",primorialBase,"#1 +",fctrlcntmns1," x ",primorialBase,"#",")!^(",primorialBase,"#) + ",primorialBase,"# x ",multiplier] Print["End of Run"] 

20151109, 23:12  #147  
Nov 2003
2^{6}×113 Posts 
Quote:
BTW, has anyone bothered to investigate the complexity of the arithmetic involved? We have a very large set of primes S = {2,3,5, ......R} for suitable R depending on the size of the final prime we are trying to construct. For billion digit primes, R = 10^500000000 Suppose we somehow (miracle?!) partition it into two sets T,U to satisfy the sqrt condition. How one does this other than a purely exponential combinatorial search is beyond me. The OP, as with all cranks ignores this question because he will find the answer to be (shall we say) inconvenient...... However, to satisfy the sqrt condition, #T will need to be very close to #U. I now suggest that the readers estimate the product of all the primes in T and U. Hint: PNT. sum of log(p) p < k ~ k. Exponentiate both sides. EACH of the products will be near e^(10^500000000 / 2) Now subtract........ The OP has presented one of the worst methods that one might imagine!!!! 

20151109, 23:16  #148 
"Rashid Naimi"
Oct 2015
Remote to Here/There
2×7×139 Posts 
The general format of the expression is:
(n#1 +m x n#)!^{(n#)} + n# x k for positive integers n, m, and k where k <= m 
20151110, 04:58  #149 
"Frank <^>"
Dec 2004
CDP Janesville
2·1,049 Posts 

20151110, 04:59  #150  
Romulan Interpreter
Jun 2011
Thailand
21344_{8} Posts 
Quote:
I don't think he has any method to show, he just tries random splits and variables, and checks if they give a prime using Wolfram or whatever. Or others here check for him. [thinking] I could try this too, but I have to think how to put some of my RL daily work in some attractive form to make the people here do my job for me, now that would be interesting, not proving primality. [/thinking] Last fiddled with by LaurV on 20151110 at 05:05 

20151110, 05:14  #151  
"Rashid Naimi"
Oct 2015
Remote to Here/There
2×7×139 Posts 
Quote:
P_{61}=283 

20151110, 05:51  #152 
Jun 2003
12AC_{16} Posts 

20151110, 06:49  #153 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3×2,399 Posts 

20151110, 07:11  #154  
"Frank <^>"
Dec 2004
CDP Janesville
2098_{10} Posts 
Quote:
ETA: Ooops! Looks like I messed up the links earlier. I thought I had done the 5121 but I didn't. Maybe start tomorrow unless someone else beats me to it. Last fiddled with by schickel on 20151110 at 07:14 Reason: SPE (Stupid poster error!) 

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