nextprime(30k)-30k exceeds gap 29.

Sat Nov 2 13:34:00 CET 2002

submitted to eis.   Cf. Subject: RE: A076150   10k+1,3,7,9.
Greeting,  I am new to this list.

nextprime(30*k)-30*k  exceeds gap 29.
that is  (30*k +1,7,11,13,17,19,23,29) are 8 x composites.
and 30*k is the (beginning) of at least 31 consecutive
composites.

Note. 1 7 11 13 17 19 23 29
are all the positive integers <30 and
 coprime to 5*3*2 = primorial 5#.

/don.mcdonald at paradise.net.nz
03.11.02  00:34
>   .user.PariGp.30k+1-29

*gp
             GP/PARI CALCULATOR Version 1.36
                 (Archimedes version)
? for(k=1,10^4,x=nextprime(30*k)-30*k;if(x>13,print(k,"*30+",x),))
42*30+17
103*30+19               GAP > 13.
151*30+17
171*30+17
192*30+19

  ***   user interrupt
? for(k=1,10^4,x=nextprime(30*k)-30*k;if(x>29,print(k,"*30+",x),))

360*30+31    is prime ...            GAP > 29.
523*30+37    is prime ...
654*30+41    is prime ...
941*30+47    is prime ...
1020*30+31   is prime ...
1047*30+59   is prime ...
1064*30+37   is prime ...
1136*30+43   is prime ...
1188*30+31
1213*30+43
1264*30+31
1280*30+31
1343*30+53
1355*30+43
1445*30+41
1477*30+41
1515*30+31
1526*30+37
1530*30+43
1533*30+31
1582*30+31
1623*30+41
1652*30+37
1693*30+31
1842*30+31
1900*30+37
1960*30+31
2018*30+49
2039*30+41
2129*30+31
2208*30+31
2280*30+37
2309*30+43
2332*30+31
2406*30+31
2413*30+31
2440*30+37
2499*30+41
2539*30+37
2622*30+31
2633*30+41
2650*30+31
2657*30+47
2708*30+41
2719*30+41
2736*30+49
2803*30+31
2842*30+37
2865*30+41
2888*30+37
2896*30+43
2990*30+53
3025*30+37
3084*30+31
3139*30+31
3189*30+31
3194*30+37
3258*30+31
3331*30+31
3352*30+31
3362*30+47
3424*30+41
3464*30+31
3475*30+31
3519*30+31
3526*30+37
3535*30+37
3552*30+31
3580*30+41
3584*30+43
3620*30+31
3656*30+37
3671*30+31
3673*30+31
3679*30+49
3702*30+31
3705*30+37
3718*30+37
3757*30+31
3795*30+41
3814*30+31
3817*30+37
3915*30+47
3966*30+47
4026*30+31
4060*30+43
4146*30+47
4162*30+37
4164*30+31
4199*30+31
4212*30+37
4229*30+43

  ***   user interrupt
*sp.
my file > *ram.sumryfact.creditcd1..  Sun,03 Nov 2002.01:21:35
by don.mcdonald.pgm.c22A. BBC Basic64.Risc os.Acorn Archimedes comp 1990.

(prob) -- #formula,--  value, --   FACTORS -- ,  (centiseconds).

datum, d
2  360*30..=10800= 2^4*3*3*3*5*5*all?n 2cs

sequence increment 1.
3  d+prob-1..=10802= 2*11*491*all?n 1cs     30 x CONSEC composites..
4  d+prob-1..=10803= 3*13*277*all?n 1cs
5  d+prob-1..=10804= 2^2*37*73*all?n 2cs
6  d+prob-1..=10805= 5*2161*all?n 2cs
7  d+prob-1..=10806= 2*3*1801*all?n 2cs
8  d+prob-1..=10807= 101*107*all?n 2cs
9  d+prob-1..=10808= 2^3*7*193*all?n 1cs
10  d+prob-1..=10809= 3*3*1201*all?n 2cs
11  d+prob-1..=10810= 2*5*23*47*all?n 2cs
12  d+prob-1..=10811= 19*569*all?n 1cs
13  d+prob-1..=10812= 2^2*3*17*53*all?n 2cs
14  d+prob-1..=10813= 11*983*all?n 2cs
15  d+prob-1..=10814= 2*5407*all?n 2cs
16  d+prob-1..=10815= 3*5*7*103*all?n 1cs
continu. 
17  d+prob-1..=10816= squareof(2^3*13*all?n 2cs
18  d+prob-1..=10817= 29*373*all?n 2cs
19  d+prob-1..=10818= 2*3*3*601*all?n 2cs
20  d+prob-1..=10819= 31*349*all?n 2cs
21  d+prob-1..=10820= 2^2*5*541*all?n 2cs
22  d+prob-1..=10821= 3*3607*all?n 2cs
23  d+prob-1..=10822= 2*7*773*all?n 1cs
24  d+prob-1..=10823= 79*137*all?n 2cs
25  d+prob-1..=10824= 2^3*3*11*41*all?n 2cs
26  d+prob-1..=10825= 5*5*433*all?n 2cs
27  d+prob-1..=10826= 2*5413*all?n 2cs
28  d+prob-1..=10827= 3*3*3*401*all?n 1cs
29  d+prob-1..=10828= 2^2*2707*all?n 2cs
30  d+prob-1..=10829= 7*7*13*17*all?n 2cs
31  d+prob-1..=10830= 2*3*5*19*19*all?n 2cs
32  d+prob-1..=10831= 10831*all?n 2cs         END OF PRIME GAP. next prime.
33  d+prob-1..=10832= 2^4*677*all?n 2cs
34  d+1..=10801= 7*1543*all?n 2cs