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Old 2022-02-07, 03:34   #34
a1call
 
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"Rashid Naimi"
Oct 2015
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Hats off to you Dr. S.

Not quite sure how you got the conclusion, but while there are plenty of "Twin-Twin-Twin-Twin" patterns based on a distance of 210 which are not divisible by any prime less than 47 (likely much higher) including 19, there is no such pattern that will not have at least one element divisible by 11.

Dirty but sufficient code.
Code:

\\EJD-100-A
theFactorial = 47! \\\Removing any of these 11's will fail to yield results
forprime(p=7503957281,19^1900,{
    if(gcd(p+2,theFactorial )<2,
        if(gcd(p+6,theFactorial )<2 && gcd(p+8,theFactorial )<2,
            if(gcd(p+30,theFactorial )<2 && gcd(p+32,theFactorial )<2 && gcd(p+36,theFactorial )<2 && gcd(p+38,theFactorial )<2,
                if (gcd(p+210,theFactorial )<2 && gcd(p+212,theFactorial )<2 /*&& gcd(p+216) && gcd(p+218) && gcd(p+240) && gcd(p+242) && gcd(p+246) && gcd(p+248)*/,
                    if( gcd(p+216,theFactorial)<2 && gcd(p+218,theFactorial)<2 && gcd(p+240,theFactorial)<2 && gcd(p+242,theFactorial)<2 && gcd(p+246,theFactorial)<2 && gcd(p+248,theFactorial)<2,
                        print("Twin-Twin-Twin-Twin");
                        print(p);
                    );
                );
            );
        );
    );
})
So 210 as a "distance" won't do.


ETA: 420 on the other hand would work:

Code:

\\EJD-110-A
theFactorial = 47! \\Removing the 11's will work for a distance of 420
forprime(p=7503957281,19^1900,{
    if(gcd(p+2,theFactorial )<2,
        if(gcd(p+6,theFactorial )<2 && gcd(p+8,theFactorial )<2,
            if(gcd(p+30,theFactorial )<2 && gcd(p+32,theFactorial )<2 && gcd(p+36,theFactorial )<2 && gcd(p+38,theFactorial )<2,
                if (gcd(p+420,theFactorial )<2 && gcd(p+422,theFactorial )<2 ,
                    if( gcd(p+426,theFactorial)<2 && gcd(p+428,theFactorial)<2 && gcd(p+450,theFactorial)<2 && gcd(p+452,theFactorial)<2 && gcd(p+456,theFactorial)<2 && gcd(p+458,theFactorial)<2,
                        print("Twin-Twin-Twin-Twin");
                        print(p);
                    );
                );
            );
        );
    );
})

Last fiddled with by a1call on 2022-02-07 at 03:53
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