OFFSET
1,1
COMMENTS
So far, I find that there exists at least one prime g, and at least one twin prime p in A001097, such that 8g + 2p is a primorial. Some of the related twin primes are rather large. The twin related to a(112), for instance, is 242 digits long. For each n, the program returns the primorial, g, g (mod 30) the twin prime (mod 30) and the twin prime. These data are in a linked file.
LINKS
Michael G. Kaarhus, Table of n, a(n) for n = 0..250
Michael G. Kaarhus, Additional data
EXAMPLE
n | b# = 8 * g + 2 * p greater or lesser
--+----------------------------------------------
1 | 5# = 8 * 2 + 2 * 7 greater
2 | 5# = 8 * 3 + 2 * 3 lesser
3 | 7# = 8 * 11 + 2 * 61 greater
4 | 7# = 8 * 19 + 2 * 29 lesser
5 | 7# = 8 * 23 + 2 * 13 greater
6 | 11# = 8 * 31 + 2 * 1031 lesser
PROG
(CALC) #!/usr/bin/calc -q -f
global b=5, chck=list(), g=1, gt, mg30=2, mg6, mp30=7, n=1, oar=pfact(b)/2,
tpr=7, ts='greatr', fmt = "%4d%s%5d%s%7d%7d%9d%11s%s%d\n";
define bookem(an) {
mp30=mod(tpr, 30);
printf(fmt, n, '.', b, '#', an, mg30, mp30, ts, ' ', tpr);
n++; append(chck, an); return(an);
}
define incg() {
top: g=nextprime(g); mg6=mod(g, 6); mg30=mod(g, 30);
if (mg30 == 13 || mg30 == 17) {goto top; }
else {gt=g*4; return(mg30); }
}
define incb(p) {b=nextprime(p); oar=pfact(b)/2; return(b); }
print;
printf(fmt, 'n', '.', 'b', '#', 'g', 'g%30', 'twin%30', 'twin type', ' ', 'twin prime');
print '----------------------------------------------------------';
for (i=0; i<=1; i++) {g=nextprime(g); bookem(g); tpr=3; ts='lesser'; mg30=3; }
b=incb(b); while (g <= b) {incg(); }
while (n <= 35) {
while (g > b) {
tpr=oar-gt;
if (tpr <= 7) {incb(b); continue; }
if (ptest(tpr, 200)) {
if (mg6 == 1 && ptest(tpr+2, 200)) {
ts='lesser'; bookem(g); break;
}
else {if (ptest(tpr-2, 200)) {
ts='greatr'; bookem(g); break;
}
}
}
incb(b);
}
incg();
while (oar-gt > 0) {b=prevprime(b); oar=pfact(b)/2; }
}
print; chs=size(chck)-1; for (i=0; i <= chs; i++) {print i+1, chck[[i]]; }
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael G. Kaarhus, Feb 12 2019
STATUS
approved