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Difference between revisions of "Conjectures 'R Us"
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==Project definition== | ==Project definition== | ||
| − | For every base ( | + | For every base ({{Vb}} ≤ 1030) for the forms {{Kbn|±|k|b|n}} there exists a unique value of {{Vk}} for each form that has been conjectured to be the lowest '[[Sierpiński number|Sierpiński value]]' (+1 form) or '[[Riesel number|Riesel value]]' (-1 form) that is composite for all values of {{Vn}} ≥ 1. {{Vk}}'s that have a trivial factor (one factor the same) for all {{Vn}}-values as well as {{Vk}}'s that make [[Generalized Fermat number]]'s are not considered. |
==Subproject #1== | ==Subproject #1== | ||
| − | Assist in proving the [[Liskovets-Gallot conjectures]] for the forms | + | Assist in proving the [[Liskovets-Gallot conjectures]] for the forms {{Kbn|±|k|2|n}} where {{Vn}} is always odd '''and''' where {{Vn}} is always even. |
==Subproject #2== | ==Subproject #2== | ||
| − | Assist in proving the | + | Assist in proving the Sierpiński base 2 2nd conjecture for the form {{Kbn|+|k|2|n}}. |
| + | |||
| + | The 1st conjectured {{Vk}} where all {{Vn}} are proven composite is {{Vk}}=78557 and is extensively tested by the [[Seventeen or Bust]] project. | ||
| + | |||
| + | The 2nd conjectured {{Vk}} where all {{Vn}} are proven composite is {{Vk}}=271129. The range of 78557 < {{Vk}} < 271129 has been extensively tested by the [[Prime Sierpiński Problem]] and [[Extended Sierpiński Problem]] projects but the projects have omitted even {{Vk}}'s from testing just like Riesel base 2 projects have. Therefore CRUS is testing even {{Vk}}'s for both the Riesel base 2 1st conjecture and Sierp base 2 2nd conjecture. | ||
==Goal== | ==Goal== | ||
| − | Prove the conjectures by finding at least one prime for all lower values of | + | Prove the conjectures by finding at least one prime for all lower values of {{Vk}}. Many of the conjectures have already been proven but much more work is needed to prove additional bases. Proving them all is not possible but we aim to prove many of them. |
==External links== | ==External links== | ||
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*[http://www.noprimeleftbehind.net/crus/tab/CRUS_tab.htm Condensed table] | *[http://www.noprimeleftbehind.net/crus/tab/CRUS_tab.htm Condensed table] | ||
*[https://primes.utm.edu/bios/page.php?id=1372 Project] at [https://primes.utm.edu/ The Prime Pages] | *[https://primes.utm.edu/bios/page.php?id=1372 Project] at [https://primes.utm.edu/ The Prime Pages] | ||
| + | {{Navbox Projects}} | ||
[[Category:Conjectures 'R Us| ]] | [[Category:Conjectures 'R Us| ]] | ||
Revision as of 11:14, 5 October 2020
Conjectures 'R Us (called CRUS in short) was established in 2007 by G.Barnes.
Project definition
For every base (b ≤ 1030) for the forms k•bn±1 there exists a unique value of k for each form that has been conjectured to be the lowest 'Sierpiński value' (+1 form) or 'Riesel value' (-1 form) that is composite for all values of n ≥ 1. k's that have a trivial factor (one factor the same) for all n-values as well as k's that make Generalized Fermat number's are not considered.
Subproject #1
Assist in proving the Liskovets-Gallot conjectures for the forms k•2n±1 where n is always odd and where n is always even.
Subproject #2
Assist in proving the Sierpiński base 2 2nd conjecture for the form k•2n+1.
The 1st conjectured k where all n are proven composite is k=78557 and is extensively tested by the Seventeen or Bust project.
The 2nd conjectured k where all n are proven composite is k=271129. The range of 78557 < k < 271129 has been extensively tested by the Prime Sierpiński Problem and Extended Sierpiński Problem projects but the projects have omitted even k's from testing just like Riesel base 2 projects have. Therefore CRUS is testing even k's for both the Riesel base 2 1st conjecture and Sierp base 2 2nd conjecture.
Goal
Prove the conjectures by finding at least one prime for all lower values of k. Many of the conjectures have already been proven but much more work is needed to prove additional bases. Proving them all is not possible but we aim to prove many of them.
External links
| Ongoing |
|
| Terminated |
