20220720, 08:17  #1 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
7^{2}×73 Posts 
Hell number formulas
A hell number formula is defined as a formula containing only small numbers and the only variable n is the exponent, and the formula only produce nonprime numbers for all small positive integers n, but not for all n (i.e. it does not have covering congruence, algebraic factorization, or combine of them)
e.g. Code:
n*2^n+1 (for n > 1) n*2^n+1 for prime n 5^n+8 (for n > 1) (18^n1)/17 (for n > 2) 4*72^n1 (72 = 2^3*3^2 is the smallest Achilles number) 4*30^n1 (for n > 3) (30 = 2*3*5 is the product of the first 3 primes) 8*48^n1 (for n > 1) (48 = 2^4*3) 3*432^n1 (432 = 2^4*3^3) 8*432^n1 (432 = 2^4*3^3) 36*48^n+1 2^nn2 (for n > 3) (2^n6)*2^n+1 (for n > 3) (2^n7)*2^n+1 12^n+1 (for n > 1) (this is special case, with Fermat number behavior, only powerof2 n can give primes) Smarandache numbers in base 4 Code:
4*9^n1 (with algebraic factorization) 4*24^n1 (with combine of coveted congruence and algebraic factorization) (2^n5)*2^n+1 (with covering congruence) (2^n2)*2^n+1 (with algebraic factorization) Last fiddled with by sweety439 on 20220720 at 18:59 
20220720, 17:12  #2 
"Matthew Anderson"
Dec 2010
Oregon, USA
3·17·23 Posts 
Interesting observation Sweety439.
Have a nice day. Matt 
20220720, 17:24  #3 
6809 > 6502
"""""""""""""""""""
Aug 2003
101ร103 Posts
24735_{8} Posts 

20220801, 23:01  #4 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
DF9_{16} Posts 

20220801, 23:03  #5 
"Forget I exist"
Jul 2009
Dumbassville
37·227 Posts 

20220806, 03:45  #6 
May 2007
Kansas; USA
10110000110110_{2} Posts 
You realize that many of these forms have primes, don't you?

20220806, 06:19  #7 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
110111111001_{2} Posts 

20220806, 07:22  #8  
May 2007
Kansas; USA
2×5,659 Posts 
Quote:
There are an infinite number of forms like this with no "small" primes. What is the point that you are trying to make? Last fiddled with by gd_barnes on 20220806 at 07:24 

20220806, 08:34  #9  
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
6771_{8} Posts 
Quote:
For the case n*2^n+1 with n>1, since it only contains the number 2, the first prime is at n=141 is unusual large, the same for 5^n+8 with n>1 whose first prime is n=95 (it corresponds to the largest minimal prime in base 5, i.e. 5^95+8, or 1(0^93)13 in base 5, see below) since it only contains 5 and 8 Also, I have a project of minimal elements for the prime strings > b written in base b, for bases 2<=b<=36, bases 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 24 are completely solved, bases 11, 22, 30 are also completely solved if strong probable primes > 10^25000 are allowed, for the data of minimal primes > b and the unsolved families, see https://github.com/xayahrainie4793/quasimepndata, the unsolved family 9{5} (i.e. 95, 955, 9555, 95555, โฆ) in base 13 contain no primes with length < 116000, but cannot be proven to only contain composites by covering congruence, algebraic factorization, or combine of them Last fiddled with by sweety439 on 20220806 at 08:36 

20220806, 10:01  #10  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
11,483 Posts 
Quote:


Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Blood and needles. ("This is gonna hurt like hell.")  Dr Sardonicus  Lounge  8  20201230 19:21 
Searching many formulas to one limit  vasyannyasha  Homework Help  4  20190625 16:37 
Big Blue Swallows Red Hell  masser  Cloud Computing  3  20181030 15:09 
Chance of finding new prime number formulas?  columbus  Information & Answers  49  20130307 22:36 
Formulas for calculating GHzdays credit  James Heinrich  PrimeNet  93  20120509 20:36 