I want to know if it is possible to distribute LL algorithm so that we can
run it on a cluster to test one exopnent on several  nodes simultaneously
so check it in a shorter peroid of time . Or should we use trial_factoring
algorithm in this regard!. or other algorithms.???

not doable. there's just WAY too much data exchanged in each pass.

each pass of the FFT used in the Lucas Lehmer algorithm crunches through something like 8MB of transform data in around 0.05 seconds (on my p4-2.5Ghz). 21 million passes later, its done. This takes about 10-12 days.

If you have a cluster of 100 such processors, the best possible thing they can do is each work on a different exponent for 10-12 days, then you'll get 100 times the throughput of a single processor.

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