20210110, 20:09  #122 
Nov 2016
B04_{16} Posts 
All known minimal primes (start with b+1) in bases 2<=b<=16: (data for bases 2, 3, 4, 5, 6, 8, 10, 12 are known to be complete)
Also three unsolved families are known: Base 11: 5777...777 Base 13: 9555...555 Base 16: DBBB...BBB 
20210110, 20:47  #123 
6809 > 6502
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Aug 2003
101×103 Posts
3·3,121 Posts 
Rather than spilling out each new thought that comes to your head when it does. Try writing them down off line and posting only 1 well formatted post every couple of days. Again think about formatting it nicely in your word processor and then making a PDF that you can later update.
I am tired of seeing you posting drival serval times a day. 
20210110, 22:21  #124 
Nov 2016
2^{2}·3·5·47 Posts 
fixed typo in the file: 3*16^n+1 should be 3*4^n+1, 12^((n+1)/2) +/ 5 should be 12^((n+2)/2) +/ 5
Last fiddled with by sweety439 on 20210111 at 12:34 
20210110, 22:45  #125 
"Curtis"
Feb 2005
Riverside, CA
1001001000011_{2} Posts 
You have an "edit" button. Use it. ONE pdf for this crap, not a new post with a new PDF every time you change a sentence. Edit the post, edit the PDF
If you were limited to one post per day on the forum, would this be it? I'm deleting your first PDF and its post. 
20210112, 18:50  #126  
Nov 2016
2^{2}·3·5·47 Posts 
Quote:
5, 7, 11, 13, 17, 19, 23, 3457, 29, 31, 13555929465559461990942712143872578804076607708197374744547, 37, 41, 43, 47, 1153, 53, 1459, 59, 61, 65537, 67, 71, 73, 2*38^2729+1, 79, 83, 3529, 89, 4051, 82823796591884729837907950243851987042491027688029791782033968173988787397927431168748344242980462637086843228831225333542602440512725127029105275975234384910715377295392116427292929375082823988662090607733781357479215392846048752706418227733688234263166843856633793191822664770551012658601887, 97, 101, 103, 107, 109, 113, 370387, 410759, 432001, 236522599840432068647134316649762315445236710001482847056204302486382634336257, 127 * The smallest prime of the form 2*b^n1: [not minimal prime (start with 2 digits) if b<=2] 3, 5, 7, 1249, 11, 13, 127, 17, 19, 241, 23, 337, 76831, 29, 31, 577, 647, 37, 20479999999999, 41, 43, 296071777, 47, 1249, 617831551, 53, 1567, 15387133080032326246081223292828787411221911122916017220126284227825703776392672467768318856009763825207593900596158761682711294895921233392537083406917227083982402321012446032594528728383203531755841, 59, 61, 2147483647, 2582935937, 67, 3676531249, 71, 73, 2887, 3041, 79, 3361, 83, 3697, 7496191, 89, 4231, 9759361, 10616831, 97, 4999, 101, 103, 14762783749438524018088313240622157671545425891033638774020213131211643094561, 107, 109, 6271, 113, 390223, 6961, 1555199999, 453961, 7687, 7937, 127 * The smallest prime of the form b^n+2 (for b == 3, 5 mod 6): [not minimal prime (start with 2 digits) if either b<=2 or b is prime, but still minimal prime (start with 2 digits) if we use LaurV's suggestion, i.e. start with b+1 instead of b] 5, 7, 11, 13, 17, 19, 23, 952809757913929, 29, 31, 1091, 37, 41, 43, 47, 885233716287722386108568808645559198522547790058305212262181780420828956357982973084581935827930464156048602918053397761948271781610736426217362565287242033121579185919812362859356307201329, 53, 1174711139839, 59, 61, 250049 * The smallest prime of the form b^n2 (for odd b): [not minimal prime (start with 2 digits) if b<=2] 7, 3, 5, 7, 14639, 11, 13, 24137567, 17, 19, 480250763996501976790165756943039, 23, 727, 839, 29, 31, 1223, 1367, 37, 2825759, 41, 43, 2207, 47, 45767944570399, 7890479, 53, 1176246293903439667999, 12117359, 59, 61 * The smallest prime of the form 3*b^n+1 (for even b): [not minimal prime (start with 2 digits) if b<=3] 7, 13, 19, 193, 31, 37, 43, 769, 17497, 61, 67, 73, 79, 40478785537, 81001, 97, 103, 109, 164617, 4801, 127, 1854365518528513, 139, 331777, 151, 157, 163, 1652195329, 10093, 181, 9678800287193699463169, 193 * The smallest prime of the form 3*b^n1 (for even b): [not minimal prime (start with 2 digits) if b<=3] 5, 11, 17, 23, 29, 431, 41, 47, 53, 59, 1451, 71, 2027, 83, 89, 108086391056891903, 101, 107, 113, 4799, 3*42^25231, 131, 137, 6911, 149, 8111, 8747, 167, 173, 179, 16913400588503030024793898903900960521239102670648159766677517992069347477035908686646316997626793866297343, 191 * The smallest prime of the form b^n+3 (for b == 2, 4 mod 6): [not minimal prime (start with 2 digits) if either b<=3 or b is prime, but still minimal prime (start with 2 digits) if we use LaurV's suggestion, i.e. start with b+1 instead of b] 5, 7, 11, 13, 17, 19, 23, 487, 29, 31, 32771, 37, 41, 43, 47, 1799519816997495209117766334283779, 53, 2707, 59, 61, 3847, 67 * The smallest prime of the form b^n3 (for b == 2, 4 mod 6): [not minimal prime (start with 2 digits) if b<=3] 5, 13, 5, 7, 11, 13, 17, 19, 23, 296196766695421, 29, 31, 54869, 37, 41, 43, 47, 1514785299052682515540398802570879414320893571359760514960122067313271212237031712057484726921232170496646835505906834446399053647478565523037279529736578428914328808517619293356029, 53, 3361, 59, 61 Last fiddled with by sweety439 on 20210112 at 19:20 

20210112, 18:59  #127  
Nov 2016
2^{2}×3×5×47 Posts 
Quote:
* repunit prime base b: {1} * generalized Fermat prime base b for even b: 1{0}1 * generalized half Fermat prime (> (b+1)/2) base b for odd b: {x}y, x = (b1)/2, y = (b+1)/2 * Williams prime with 1st kind base b: x{y}, x = b2, y = b1 * Williams prime with 2nd kind base b: x{0}1, x = b1 * Williams prime with 4th kind base b: 11{0}1 (not minimal prime if there is smaller prime of the form 1{0}1 * dual Williams prime with 1st kind base b: {x}1, x = b1 * dual Williams prime with 2nd kind base b: 1{0}x, x = b1 * dual Williams prime with 4th kind base b: 1{0}11 (not minimal prime if there is smaller prime of the form 1{0}1 * prime of the form 2*b^n+1 for bases b>2: 2{0}1 * prime of the form 2*b^n1 for bases b>2: 1{x}, x = b1 * prime of the form b^n+2 for bases b>2 with gcd(b,2)=1: 1{0}2 * prime of the form b^n2 for bases b>2 with gcd(b,2)=1: {x}y, x = b1, y = b2 * prime of the form 3*b^n+1 for bases b>3: 3{0}1 * prime of the form 3*b^n1 for bases b>3: 2{x}, x = b1 * prime of the form b^n+3 for bases b>3 with gcd(b,3)=1: 1{0}3 * prime of the form b^n3 for bases b>3 with gcd(b,3)=1: {x}y, x = b1, y = b3 * prime of the form 4*b^n+1 for bases b>4: 4{0}1 * prime of the form 4*b^n1 for bases b>4: 3{x}, x = b1 * prime of the form b^n+4 for bases b>4 with gcd(b,4)=1: 1{0}4 * prime of the form b^n4 for bases b>4 with gcd(b,4)=1: {x}y, x = b1, y = b4 * prime of the form k*b^n+1 for fixed 1<=k<=b1 (i.e. the prime for the CRUS Sierpinski conjecture for fixed 1<=k<=b1): k{0}1 * prime of the form k*b^n1 for fixed 1<=k<=b1 (i.e. the prime for the CRUS Riesel conjecture for fixed 1<=k<=b1): x{y}, x = k1, y = b1 * prime of the form b^n+k for fixed 1<=k<=b1: 1{0}k * prime of the form b^nk for fixed 1<=k<=b1: {x}y, x = b1, y = bk * prime of the form (k*b^n1)/gcd(k1,b1) for fixed k with 0<=(k1)/gcd(k1,b1)<=b1: x{y}, x = (k1)/gcd(k1,b1), y = (b1)/gcd(k1,b1) * prime of the form (b^nk)/gcd(k1,b1) for fixed k with gcd(b,k) = 1 and 0<=k<=b1: x = (b1)/gcd(k1,b1), y = (bk)/gcd(k1,b1) 

20210112, 19:03  #128 
Nov 2016
2^{2}·3·5·47 Posts 
This puzzle is an extension of the original minimal prime base b puzzle, to include CRUS Sierpinski/Riesel conjectures base b with kvalues < b, i.e. the smallest prime of the form k*b^n+1 and k*b^n1 for all k < b
Also include the dual Sierpinski/Riesel conjectures (of course in the dual case, gcd(k,b) = 1 is needed) base b with kvalues < b, i.e. the smallest prime of the form b^n+k and b^nk for all k < b 
20210112, 19:09  #129  
Nov 2016
2^{2}·3·5·47 Posts 
Quote:
7, 23, 47, 79, 14639, 167, 223, 24137567, 359, 439, 480250763996501976790165756943039, 6103515623, 727, 839, 29789, 1087, 1223, 1367, 2313439, 2825759, 1847, 1532278301220703123, 2207, 2399, 45767944570399, 7890479, 3023, 1176246293903439667999, 12117359, 3719, 3967 and the OEIS sequence for the exponent (n) should be A250200, not A255707 Also the b^23 case (also should require n>1): 5, 13, 61, 97, 193, 4093, 397, 113379901, 673, 296196766695421, 1021, 1153, 54869, 1597, 1933, 2113, 476837158203124999999999999999999997, 1514785299052682515540398802570879414320893571359760514960122067313271212237031712057484726921232170496646835505906834446399053647478565523037279529736578428914328808517619293356029, 29334891491018187280695810850813, 3361, 916132829, 4093 Last fiddled with by sweety439 on 20210113 at 18:07 

20210113, 15:57  #130  
Nov 2016
2820_{10} Posts 
Quote:
Its formula is (206*16^3223411)/15 This number is like the largest minimal prime (start with 2 digits) in base 16 The families 5{7} (base 11) and 9{5} (base 13) still no (probable) prime found. The formulas of these two families are (57*11^n7)/10 and (113*13^n5)/12, respectively. Last fiddled with by sweety439 on 20210216 at 14:17 

20210113, 16:48  #131 
Nov 2016
2^{2}·3·5·47 Posts 
Last fiddled with by sweety439 on 20210219 at 07:36 
20210113, 16:58  #132 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
3×3,121 Posts 
Since you have mod rights in this area, you can delete the previous PDF and replace it with the current. Keeping an up to date file and the first post of the thread is a common way of handling things like this. There is no need to post about a new item that will then be added to the pdf. Just update the file. Then maybe 1 time a week give a one line summary for each type of item updated. Less stuff to search through and better organization might make this more useful.

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