Więc tak od początku...Nie jestem matematykiem ani zawodowo ani hobbystycznie.Naukę zakończyłem jako mgr.(automatyk-elektryk). Programuję w C++ w wolnym czasie.Podczas pisania kalkulatora "bignum" zauważyłem coś ciekawego.Potrafię to zapisać jako twierdzenie:
Dla każdego systemu numerycznego jeżeli odwrotność (1/n) liczby naturalnej n ma okresowość n-1 cyfr to n jest liczbą pierwszą.
Nie potrafię tego potwierdzić ani zaprzeczyć więc potrzebowałbym konsultacji matematyka.
Przykłady:(pierwsza liczba to system liczbowy,następne to liczby pierwsze dla których zasada ma zastosowanie)
2-1,3,5,11,13,19,29,37,53,59,61,67,83,101,107,131,139,149,163,
3-1,5,7,17,19,29,31,43,53,79,89,101,113,127,137,139,149,163,
4-1,
5-1,3,7,17,23,37,43,47,53,73,83,97,103,107,113,137,157,167,
6-1,11,13,17,41,59,61,79,83,89,103,107,109,113,127,131,137,151,157,
7-1,5,11,13,17,23,41,61,67,71,79,89,97,101,107,127,151,163,
8-1,3,5,11,29,53,59,83,101,107,131,149,
9-1,
10-1,7,17,19,23,29,47,59,61,97,109,113,131,149,167,
11-1,3,13,17,23,29,31,41,47,59,67,71,73,101,103,109,149,163,
12-1,5,7,17,31,41,43,53,67,101,103,113,127,137,139,149,151,163,
13-1,5,11,19,31,37,41,47,59,67,71,73,83,89,97,109,137,149,151,167,
14-1,3,17,19,23,29,53,59,73,83,89,97,109,127,131,149,151,
15-1,13,19,23,29,37,41,47,73,83,89,97,101,107,139,149,151,157,167,
16-1,
17-1,3,5,7,11,23,31,37,41,61,97,107,113,131,139,167,
18-1,5,11,29,37,43,53,59,61,67,83,101,107,109,139,149,157,163,
19-1,7,11,13,23,29,37,41,43,47,53,83,89,113,139,163,
20-1,3,13,17,23,37,43,47,53,67,73,83,103,107,113,137,157,163,167,
21-1,19,23,29,31,53,71,97,103,107,113,137,139,149,157,
22-1,5,17,19,31,37,41,47,53,71,83,107,131,139,
23-1,3,5,17,47,59,89,97,113,127,131,137,149,167,
24-1,7,11,13,17,31,37,41,59,83,89,107,109,113,137,157,
25-1,
26-1,3,7,29,41,43,47,53,61,73,89,97,101,107,131,137,139,157,167,
27-1,5,17,29,53,89,101,113,137,149,
28-1,5,11,13,17,23,41,43,67,71,73,79,89,101,107,
29-1,3,11,17,19,41,43,47,73,79,89,97,101,113,127,131,137,163,
30-1,11,23,41,43,47,59,61,79,89,109,131,151,167,
31-1,7,17,29,47,53,59,61,67,71,73,89,107,131,137,
32-1,3,5,13,19,29,37,53,59,67,83,107,139,149,163,
33-1,5,7,13,19,23,43,47,53,59,71,73,89,113,137,
34-1,19,23,31,41,43,53,59,67,73,79,83,101,113,149,157,167,
35-1,3,11,37,41,47,53,61,71,79,83,89,101,103,137,151,167,
36-1,
37-1,5,13,17,23,29,59,79,97,109,113,131,167,
38-1,3,5,7,23,47,59,89,97,101,107,113,149,157,
39-1,11,17,29,37,47,53,59,73,79,83,97,109,113,127,167,
40-1,7,11,17,19,23,29,47,59,73,97,101,103,109,131,137,139,149,167,
41-1,3,11,13,17,19,47,53,67,89,97,149,167,
42-1,5,23,31,37,59,71,73,83,101,109,137,163,
43-1,5,23,29,31,47,59,61,79,83,89,103,107,113,127,137,149,157,167,
44-1,3,17,23,29,31,47,59,61,67,71,73,103,109,163,
45-1,7,13,17,47,53,73,83,103,107,113,127,137,163,167,
46-1,11,13,17,43,67,83,89,101,107,113,127,137,167,
47-1,3,5,7,29,41,59,71,73,79,83,109,113,137,
48-1,5,17,19,29,31,41,43,53,67,79,89,101,103,127,137,149,151,
49-1,
50-1,3,11,13,29,37,53,59,67,83,101,107,109,131,139,149,163,
51-1,11,19,23,53,61,67,89,101,103,107,109,137,149,151,167,
52-1,5,7,11,19,31,37,41,47,59,71,83,109,137,149,151,163,167,
53-1,3,5,19,23,31,41,71,73,79,83,101,103,109,127,137,139,157,167,
54-1,7,13,17,37,41,59,61,79,83,89,103,107,113,131,137,151,
55-1,29,31,37,43,53,59,61,71,83,101,107,113,127,137,149,157,167,
56-1,3,17,23,29,37,41,53,59,71,83,89,97,109,127,131,139,149,151,
57-1,5,11,17,23,37,47,67,83,97,109,127,131,137,149,
58-1,5,13,17,41,47,53,73,83,89,97,107,109,113,127,137,139,149,
59-1,3,7,13,19,37,61,71,73,79,89,97,101,107,109,113,149,167,
60-1,19,23,29,41,47,73,79,83,89,97,107,149,157,167,
61-1,7,11,17,23,29,37,43,53,59,67,71,89,101,139,151,157,
62-1,3,5,11,17,43,47,71,73,83,89,103,109,137,149,157,
63-1,5,11,13,17,23,41,43,61,67,71,79,89,101,107,151,157,163,
64-1,
65-1,3,17,23,31,41,53,59,71,89,103,107,109,127,149,
66-1,7,23,29,47,79,83,89,101,107,113,131,137,149,157,163,
67-1,5,13,19,23,41,47,53,59,61,71,83,101,103,107,109,113,127,131,137,163,167,
68-1,3,5,7,11,29,61,71,73,79,97,107,113,139,163,167,
69-1,29,37,41,43,47,59,67,71,109,157,167,
70-1,19,41,47,59,79,89,103,107,109,113,137,139,149,157,163,167,
71-1,3,13,17,19,41,43,53,61,83,97,103,107,137,149,151,167,
72-1,5,11,13,19,29,37,43,53,59,83,101,107,109,131,139,149,157,163,
73-1,5,7,11,17,29,31,43,47,53,59,83,101,107,139,157,163,167,
74-1,3,11,17,23,31,53,67,79,83,89,97,101,103,107,113,149,157,167,
75-1,7,17,31,41,53,79,89,101,103,113,137,149,163,
76-1,13,23,29,37,41,43,47,83,89,97,113,131,163,
77-1,3,5,29,43,47,59,79,103,107,149,151,157,
78-1,5,17,19,47,61,67,71,73,103,107,127,149,167,
79-1,11,17,19,23,29,31,37,53,61,67,83,109,113,137,149,163,167,
80-1,3,7,13,17,23,47,53,67,83,97,107,113,137,157,163,167,
81-1,
82-1,5,7,17,47,59,71,79,89,97,107,131,137,151,163,167,
83-1,3,5,11,23,31,59,89,97,101,127,131,137,149,157,167,
84-1,11,13,23,29,31,53,71,73,97,103,107,113,137,149,157,
85-1,11,13,29,47,53,67,79,83,103,109,127,131,137,139,157,
86-1,3,19,23,31,47,53,73,79,89,101,103,113,127,137,167,
87-1,5,7,37,47,53,61,67,73,97,103,131,149,157,
88-1,5,17,23,41,47,53,73,83,103,107,131,139,157,
89-1,3,7,13,19,23,29,37,41,43,59,83,101,113,137,149,151,163,
90-1,11,17,19,23,29,47,59,97,101,113,131,137,139,149,167,
91-1,17,19,37,43,47,59,61,83,107,109,127,137,149,157,167,
92-1,3,5,17,37,47,53,59,61,71,89,97,113,127,137,139,149,163,167,
93-1,5,13,37,41,59,71,73,101,107,113,127,131,139,149,151,
94-1,7,11,37,41,53,101,107,113,137,149,157,163,
95-1,3,11,17,29,41,67,89,107,109,131,137,157,167,
96-1,7,11,17,31,37,59,61,83,89,103,107,109,113,127,131,151,157,
97-1,5,13,17,19,23,29,41,59,83,107,127,131,137,149,157,
98-1,3,5,13,19,29,37,43,53,59,67,83,101,107,109,131,139,149,
99-1,17,23,41,47,59,67,71,73,101,103,109,149,
100-1,
101-1,3,7,11,29,41,53,59,67,73,83,103,113,127,139,149,163,167,
102-1,5,13,23,29,59,71,73,83,89,97,137,139,151,157,167,
103-1,5,7,23,53,59,83,89,101,107,109,113,131,163,167,
104-1,3,31,41,43,47,53,61,71,73,89,97,101,107,131,137,139,151,157,167,
105-1,11,17,19,29,31,43,47,61,83,167,
106-1,11,13,23,29,31,37,41,43,59,71,73,127,131,137,149,151,163,167,
107-1,3,5,11,17,23,47,73,79,83,97,113,163,
108-1,5,7,17,19,29,41,53,67,79,89,101,103,113,137,139,149,151,163,
109-1,17,19,23,37,47,53,59,79,101,103,107,127,139,149,151,163,167,
110-1,3,7,13,19,31,41,97,113,127,131,137,139,167,
111-1,13,23,41,53,59,67,97,131,137,139,149,151,167,
112-1,5,11,17,23,41,43,61,73,89,97,101,107,127,151,163,
113-1,3,5,17,23,29,37,47,59,67,71,73,79,89,101,107,137,167,
114-1,17,29,31,43,47,53,59,79,97,103,107,127,137,139,151,157,163,
115-1,7,13,31,43,59,61,67,71,73,83,89,103,107,109,131,139,149,151,
116-1,3,11,17,19,37,41,43,47,61,79,89,101,113,127,131,137,163,
117-1,5,7,11,19,31,41,47,67,73,83,89,137,149,151,163,167,
118-1,5,11,29,53,67,71,73,79,83,89,97,113,127,131,167,
119-1,3,13,29,43,89,101,109,113,131,139,157,167,
120-1,23,43,47,53,59,61,73,89,97,109,131,151,163,167,
121-1,
122-1,3,5,7,17,23,79,83,89,107,109,131,149,163,
123-1,5,11,13,47,71,97,103,109,113,139,157,167,
124-1,7,13,17,19,29,37,47,53,59,61,67,71,89,103,107,131,137,163,
125-1,3,17,23,47,53,83,107,113,137,167,
126-1,17,23,29,37,53,59,71,73,79,83,97,131,139,149,151,
127-1,5,11,19,29,31,47,53,71,79,89,101,107,109,131,
128-1,3,5,11,13,19,37,53,59,61,67,83,101,107,131,139,149,163,
129-1,7,11,17,19,23,37,41,47,59,61,83,101,107,151,163,167,
130-1,17,23,29,37,41,67,71,83,89,101,113,127,139,151,163,
131-1,3,7,17,29,37,59,73,107,137,149,157,167,
132-1,5,13,23,43,47,53,59,61,71,73,79,89,113,137,139,
133-1,5,17,37,47,53,71,73,79,83,107,109,113,127,131,151,157,
134-1,3,11,23,29,41,43,47,71,97,113,127,137,139,149,151,167,
135-1,19,23,29,31,37,41,47,73,83,89,97,101,107,139,149,167,
136-1,7,13,19,23,31,41,59,67,71,83,97,101,113,149,157,167,
137-1,3,5,13,29,31,47,53,83,89,97,113,131,149,157,163,
138-1,5,7,11,41,47,53,71,79,83,97,103,107,149,167,
139-1,11,17,47,53,61,71,79,83,101,107,109,127,131,149,157,163,167,
140-1,3,11,41,53,61,71,83,89,113,137,151,167,
141-1,13,17,31,43,53,59,67,73,83,101,127,131,139,149,151,
142-1,5,17,29,41,59,79,113,137,139,157,167,
143-1,3,5,7,17,19,23,29,37,83,89,101,103,137,167,
144-1,
145-1,7,11,13,23,31,41,53,67,79,83,89,107,131,167,
146-1,3,17,19,31,37,47,67,103,109,113,149,151,167,
147-1,5,17,19,29,41,43,53,67,79,89,101,103,113,149,163,
148-1,5,17,19,23,29,31,43,59,61,89,103,109,131,163,167,
149-1,3,11,13,23,41,43,59,71,79,83,89,101,109,137,163,167,
150-1,7,11,13,17,37,59,83,89,107,113,127,137,
151-1,11,41,47,53,59,73,89,101,103,109,113,139,149,157,167,
152-1,3,5,7,23,41,47,59,61,67,89,101,107,113,149,157,
153-1,5,23,29,37,41,61,71,79,97,107,109,131,163,167,
154-1,13,19,47,53,67,79,83,89,97,101,103,131,139,163,
155-1,3,19,23,29,43,59,71,83,89,97,167,
156-1,11,17,29,47,53,59,79,83,97,101,103,109,113,127,139,167,
157-1,5,7,23,41,43,53,59,61,73,83,97,103,107,131,137,139,149,151,
158-1,3,5,13,17,23,31,41,43,59,107,113,137,139,151,167,
159-1,7,17,23,29,43,73,83,89,109,113,149,163,167,
160-1,11,17,29,47,59,73,101,109,113,131,137,139,149,167,
161-1,3,11,37,47,53,59,73,79,107,109,131,137,139,149,167,
162-1,5,11,13,19,43,53,59,67,83,101,107,109,131,149,157,
163-1,5,13,17,29,37,43,47,71,83,89,137,149,151,157,167,
164-1,3,7,17,29,47,53,71,79,89,101,137,149,151,167,
165-1,17,19,37,59,61,67,79,89,97,103,107,109,139,151,163,167,
166-1,7,19,23,29,31,37,61,67,73,107,109,127,137,151,163,
167-1,3,5,11,13,17,19,31,37,47,53,101,107,109,113,149,
168-1,5,23,31,37,59,67,83,97,101,103,109,113,131,137,
169-1,
170-1,3,37,41,47,59,71,103,107,127,137,149,163,
171-1,7,11,13,23,29,41,47,53,83,89,97,109,113,131,139,
172-1,5,11,23,29,31,37,47,59,73,83,89,107,113,127,137,149,157,167,
173-1,3,5,7,11,17,19,53,59,61,71,97,101,103,107,127,
174-1,19,47,59,73,83,101,103,107,109,163,
175-1,13,17,23,41,43,67,71,73,89,101,107,127,157,163,
176-1,3,13,17,23,29,31,41,47,61,101,109,149,
177-1,5,17,29,31,41,43,53,61,71,73,97,103,107,137,157,167,
178-1,5,7,11,23,53,67,103,107,109,157,
179-1,3,31,41,47,53,59,73,83,97,107,109,113,137,139,
180-1,7,13,17,23,37,47,53,67,73,83,97,103,107,113,127,137,167,
181-1,17,19,23,41,47,53,61,83,89,97,103,107,109,113,131,149,151,157,163,
182-1,3,5,11,17,23,29,47,67,127,137,163,167,
183-1,5,11,37,41,59,113,127,137,149,157,163,
184-1,11,13,17,19,29,43,47,67,71,83,89,97,101,107,127,137,167,
185-1,3,7,19,29,47,53,59,61,67,73,83,89,107,127,131,137,
186-1,19,41,47,53,71,73,79,83,151,
187-1,5,7,37,59,79,97,101,103,107,113,131,149,167,
188-1,3,5,13,29,41,59,73,79,83,103,109,113,131,137,
189-1,11,13,23,29,31,61,71,97,103,107,113,137,139,149,
190-1,17,37,41,43,53,59,61,73,83,101,103,137,149,167,
191-1,3,23,43,53,59,67,73,89,101,103,107,137,157,
192-1,5,7,17,19,29,41,43,53,79,89,113,127,137,139,149,163,
193-1,5,11,13,17,19,29,41,47,53,61,73,79,89,113,167,
194-1,3,7,11,17,23,41,53,71,101,109,127,137,
195-1,11,23,29,59,67,71,79,101,107,137,139,157,163,
196-1,
197-1,3,5,13,17,31,67,71,79,89,113,131,139,149,167,
198-1,5,17,23,31,37,41,43,47,53,71,83,107,131,
199-1,7,17,23,31,41,47,73,97,101,103,113,137,149,151,
200-1,3,11,19,29,37,43,53,59,61,83,101,107,109,139,149,157,
Użytkownik piastlis edytował ten post 22.10.2016 - 09:32