C (gcc), 87 86 bytes

Saved a byte thanks to the man himself Arnauld!!!

i;q;p;m;f(b){for(p=m=b;p|!q;++m)for(q=p=i=1;++i<m;p=p&&m%i)q=m%i?q:q&&b*~-b*~b%i;--m;}

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Port of my Python answer.

C (gcc), 87 86 84 bytes

Saved a byte thanks to the man himself Arnauld!!!

i;q;p;m;f(b){for(p=m=b;p|!q;++m)for(q=p=i=1;++i<m;)q=m%i<1?p=0,q&&b*~-b*~b%i:q;--m;}

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Port of my Python answer.

C (gcc), 87 bytes

i;q;p;m;f(b){for(p=m=b;p|!q;++m)for(q=p=i=1;++i<m;p=p&&m%i)q=m%i?q:q&&(b*b*b-b)%i;--m;}

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Port of my Python answer.

C (gcc), 87 86 bytes

Saved a byte thanks to the man himself Arnauld!!!

i;q;p;m;f(b){for(p=m=b;p|!q;++m)for(q=p=i=1;++i<m;p=p&&m%i)q=m%i?q:q&&b*~-b*~b%i;--m;}

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Port of my Python answer.

C (gcc), 91 bytes

i;q;p;m;f(b){for(q=0,p=m=b;p|!q;++m)for(q=p=i=1;++i<m;p=p&&m%i)q=m%i?q:q&&(b*b*b-b)%i;--m;}

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Port of my Python answer.

C (gcc), 87 bytes

i;q;p;m;f(b){for(p=m=b;p|!q;++m)for(q=p=i=1;++i<m;p=p&&m%i)q=m%i?q:q&&(b*b*b-b)%i;--m;}

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Port of my Python answer.