Primes, families of, arranged in sets of primeth recursions --
Initial primes of such sets :-
ord. |
card. |
prod. |
1^{st} |
2 |
2 |
2^{nd} |
7 |
14 |
3^{rd} |
13 |
39 |
4^{th} |
19 |
76 |
5^{th} |
23 |
115 |
6^{th} |
29 |
174 |
7^{th} |
37 |
259 |
8^{th} |
43 |
344 |
9^{th} |
47 |
423 |
10^{th} |
53 |
530 |
11^{th} |
61 |
671 |
12^{th} |
71 |
852 |
13^{th} |
73 |
949 |
14^{th} |
79 |
1106 |
15^{th} |
89 |
1335 |
16^{th} |
97 |
1552 |
17^{th} |
101 |
1717 |
18^{th} |
103 |
1824 |
19^{th} |
107 |
1963 |
20^{th} |
113 |
2260 |
[note the years 1963 (JFK) and (in the Coptic calendar) 1717 (WTC).]
2; 7; 13; 19; 23, 29, 37, 43, 47, 53, 61, 71, 73, 79, 89, 97, 101, 103, 107, 113, ...
(These primeth-recursion sets are :-
2, 3, 5, 11, 31, 127, 709, ...;
7, 17, 59, 277, ...;
13, 41, 179, ...;
19, 67, 331, ...;
23, 83, 431, ...;
29, 109, ...;
37, 157, ...;
43, 191, ...;
47, 221, ...;
53, 241, ...;
61, 283, ...;
71, 353, ...;
73, 367, ...;
79, 401, ...;
89, 461, ...;
97, 509, ...,
101, 547, ...
103, 563, ...;
107, 587, ...;
113, 617, ...;
...)
19
(Stated in terms to the base of the initial prime of each such set, the sets are :-
2, 2+1 (=2^2-1), 2^2+1, 2^3+2+1, 2^4+2^3+2^2+2+1 (=2^5-1), 2^7+2^6+2^5+2^4+2^3+2^2+2+1 (=2^8-1), 2^9+2^7+2^6+2^2+1, ... [the 2^{nd} is 2^2-1; the 5^{th} is 2^5-1; the 6^{th} is 2^8-1]
7, 7*2+3, 7^2+7+3, (7^2)*5+7*4+4 (= 7^3-7^2-7*3-3), ...
13, 13*3+2, 13^2+10, ...
19, 19*3+10, ...
[written Dec 26^{th} Mon 2011]
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[found, two days later, in The On-Line Encyclopedia of Integer Sequences http://oeis.org ]
A007821 Primes p(n) where n runs through the nonprimes. +100
25
2, 7, 13, 19, 23, 29, 37, 43, 47, 53, 61, 71, 73, 79, 89, 97, 101, 103, 107, 113, 131, 137, 139, 149, 151, 163, 167, 173, 181, 193, 197, 199, 223, 227, 229, 233, 239, 251, 257, 263, 269, 271, 281, 293, 307, 311, 313, 317, 337, 347, 349, 359, 373
A088982 Primes that are between consecutive prime-indexed-primes. +90
0
7, 13, 19, 23, 29, 37, 43, 47, 53, 61, 71, 73, 79, 89, 97, 101, 103, 107, 113, 131, 137, 139, 149, 151, 163, 167, 173, 181, 193, 197, 199, 223, 227, 229, 233, 239, 251, 257, 263, 269, 271, 281, 293, 307, 311, 313, 317, 337, 347, 349, 359, 373, 379, 383, 389
The ordinals of these primes are listed at http://oeis.org/A007821/b007821.txt
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[written Jan 5 (Thur) 2012]
N.B. 13 * 220 = 2260 = 2012 (praedicted year of mass-landings of the UFOs) + 248 :-"the Torah ... contains two hundred and forty-eight commandments, corresponding to the number of the members of thy body" (Ginzberg, Legends of the Jews, p. 384).
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