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Problems & Puzzles:
Puzzles
Puzzle 1274 A
modified Buss's Conjecture
On June 25, 2026, Davide Rotondo sent a new
Conjecture & Puzzle:
This is my last conjecture regarding Buss.
References,
1
&
2
Construct the following Table according to the
following algorithm:
Start with f(1)=1.
Calculate the smallest
prime number obtained by concatenating the smallest
number (other than 1) to f(n).
Calculate
R(n) based on the value used in the concatenation to
obtain that prime number.
Calculate f(n+1)
= f(n)R(n).
Here are the first ten rows:
|
f(n) |
Smallest prime number obtained
by concatenating the
smallest
number
(other than 1) to f(n) |
R(n) |
|
1 |
1(3) |
3 |
|
3 |
3(7) |
7 |
|
21 |
21(11) |
11 |
|
231 |
231(17) |
17 |
|
3927 |
3927(23) |
23 |
|
90321 |
90321(19) |
19 |
|
1716099 |
1716099(13) |
13 |
|
22309287 |
22309287(29) |
29 |
|
646969323 |
646969323(37) |
37 |
|
2.3938E+10 |
23937864951(41) |
41 |
Davide Rotondo conjectures that the
third column will display all and only odd prime
integers (except 5) withou any repetition.
He has calulated the following values for
the third column, R(n):
[3, 7, 11, 17, 23,
19, 13, 29, 37, 41,
67, 53, 71, 47, 97,
109, 113, 107, 31,
151, 59, 73, 127,
43, 131, 101, 137,
157, 103, 227, 149,
181, 223, 193, 211,
241, 167, 251, 79,
83, 163, 347, 197,
173, 293, 263, 367,
307, 257, 463, 383,
239, 179, 419, 571,
577, 283, 89, 373,
823, 379, 233, 541,
929, 617, 619, 631,
709, 673, 1231, 547,
199, 947, 1171, 449,
397, 311, 953, 349,
191, 409, 139, 317,
601, 431, 271, 457,
613, 509, 719, 811,
647, 659, 967]
Q1. Can you
verify at least the Rotondo's list up to 967
Q2. Can you extend your list and after the end of
your list name the smallest prime absent
Q3.
Can you prove the Rotondo's conjecture
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