A FIBONACCI-PRIME NUMBER RELATION
B . B . SHARPE
State University of New York at Buffalo
Fibonacci n u m b e r s m a y b e r e l a t e d to p r i m e n u m b e r s as follows:
Conjecture.
1.
F . + F . will be a p r i m e n u m b e r for at l e a s t one value of i, p r o -
vided i + j is a p r i m e n u m b e r .
2.
F . - F . will be a p r i m e n u m b e r for at l e a s t one value of i, p r o i
J
vided i + j is p r i m e and g r e a t e r than 3 (i > j). An initial verification:
l+j
F.+F.
F.-F.
i
J
1 J
2
F
3
F
l+Fl =
2
5
2+Fl = 2
F3+F2 = 3
F
4-Fl =
2
7
F
4+F3 =
F
6'F1 =
7
11
F
6
13
V 4
5
6"F5 =
F7-F6= 5
5=13
F = 37
17
Fn+F6=97
19
F
23
10+F9 = 89
F12+F11=233
29
F17+F12-1741
31
37
Fl6+F15=1597
F 2 4 + F 1 3 = 46601
41
F 3 0 + F n = 832129
43
F 2 4 + F 1 9 = 50549
47
F
27+F20
53
F
29+F24^560597
=
3
F
+ F
203183
F - F = 13
*9
8
F - F =: 131
*12 7
F - F == 2579
18 5
F
-F
*17
12 = 1453
F
-F
^ 1 8 r 1 3 = 2351
F - F == 317877
*28
9
F
-F
*24
17 = 44771
F
-F
* 24 19 = 42187
r
27~
20
= 189653
No further verification is p o s s i b l e using L e h m e r ' s F a c t o r Table
to 10, 000, 000.
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