2 · 7⁷⁰⁹⁹⁷⁶ + 2 · 7²¹¹⁴⁴¹ + 1

This prime's information:

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Lei Zhou writes (18 Feb 2023):  (report abuse)

This is a balanced base 7 prime with 3 non-zero digits. p-1=2^4*7^211441*11*191*Phi[199414,7]*Phi[997070,7] Using prime number 2,7,11,191 as helper, OpenPFGW provides that it is a Fermat and Lucas PRP: Using F=2^4*7^211441*11*191 and G=6, CHG pari script proved that this is a prime number. (full CHG output is too long to be posted here. Verification is the following) The result is certified by David Broadhurst's verifier chgcertd.gp. Testing a PRP called "cp_709976_+7_211441_c2+1.in". Pol[1, 1] with [h, u]=[4, 1] has ratio=1.3326166955388196603 E-114759 at X, ratio=2.6719307693795337093 E-101686 at Y, witness=2. Pol[2, 1] with [h, u]=[6, 2] has ratio=1.0266956398373537968 E-13069 at X, ratio=1.7937756553937938483 E-50848 at Y, witness=2. Pol[1, 2] with [h, u]=[4, 1] has ratio=4.442055651796065534 E-114760 at X, ratio=2.6719307693795337093 E-101686 at Y, witness=2. Pol[2, 2] with [h, u]=[6, 2] has ratio=1.0266956398373537968 E-13069 at X, ratio=5.381326966181381545 E-50848 at Y, witness=2. Validated in 4 sec. The certificate is available at here.

Verification data:

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