New prime found: 2^74015*3^42*35^8*5863^16*137^73952*953^2*1223^4*15217 – ((((3643*121875747021497257)^2*19568-1)^2*7624+1)^2*273906-1)

Using Primo, 274^2311 – 83 is proven a prime number.
Define this as p[1]=a[1]-b[1], while a[1]=274^2311 and b[1]=83.
p[2]=16236*(a[1]^2-b[1]^2)-1
=16236*274^4622 – 111849805
is proven prime using pfgw:
pfgw -h”p[1]” -tp “p[2]”

Keep going in this way, it is obtained:
p[3]=2^9249*3^5*5*7*11^2*13^2*41^2*137^9244 – (3643*121875747021497257)
p[4]=2^18502*3^10*5^2*7^2*11^4*13^4*41^4*137^18488*1223 – ((3643*121875747021497257)^2*19568-1)
p[5]=2^37007*3^20*35^4*5863^8*137^36976*953*1223^2 – (((3643*121875747021497257)^2*19568-1)^2*7624+1)
p[6]=2^74015*3^42*35^8*5863^16*137^73952*953^2*1223^4*15217 – ((((3643*121875747021497257)^2*19568-1)^2*7624+1)^2*273906-1)

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