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smallest n such that (5*2^k)*(5^2*2^3)+1 is prime for k = 0 to k = 3 (Sierpinski problem base 148, k = 5, 5*2 (=X), 5*4 (=18), 5*8 (=34)) smallest n such that (7*2^k)*(7^2*2^3)−1 is prime for k = 0 to k = 3 (Riesel problem base 288, k = 7, 7*2 (=12), 7*4 (=24), 7*8 (=48))
k=0 (5*148^n+1), n=53E (2nd) k=0 (7*288^n−1), n unknown (4th, unknown)
k=1 (X*148^n+1), n=35E0 (3rd) k=1 (12*288^n−1), n=8 (1st)
k=2 (18*148^n+1), n=1 (1st) k=2 (24*288^n−1), n=X5327 (3rd)
k=3 (34*148^n+1), n unknown (4th, unknown) k=3 (48*288^n−1), n=12732 (2nd)

The dual of k=0 is k=3, the dual of k=1 is k=2, the dual of k=2 is k=1, the dual of k=3 is k=0

For both bases (S148 and R288), the dual of 1st is 3rd, the dual of 2nd is 4th

S148 the k is nth if and only if R288 the (3−k) is nth

R288 the k is nth if and only if S148 the (3−k) is nth

Note that 5+7 = 10 and 5,7 are both primes, and 5,7 are the only primes not dividing 10 between 1 and 10−1

2&3[]

900*6^?+1 (GFN)

10*10^?+1 (GFN)

30*40^?+1

100*140^2+1

400*540^?+1

16*1000^?+1

690*30^11−1

800*30^144−1

6*40^206-1

280*40^?-1

20*54^18E8-1

2*60^2X-1

3*60^2−1

4*60^460089-1

16*60^X46-1

20*60^1648-1

30*60^1−1

3*90^1X6+1

6*90^9539+1

2*100^20-1

6*100^552+1

3*300^9316-1

8*300^?-1

20*509^725X2-1

6*540^?-1

2*800^?-1

3*800^?-1

3*1000^?-1

2&5[]

34*5^724+1

X*148^35E0+1

18*148^1+1

X*568^88X8+1

8*68^2-1

X*68^?-1

4*568^176E9-1

5*568^EX50-1

8*568^?-1

21*568^60209-1

2&3&5[]

26*10^100+1

10*26^713+1

20*39^X876+1

20*39^748E7-1

2&7[]

7*288^?-1

12*288^8-1

24*288^X3527-1

48*288^12732-1

2&3&7[]

3*36^1563-1

12*36^1-1

3*1030^?-1

12*1030^?-1

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