Pentagonals (P(2), P(A), P(B)) in arithmetic progression

If $P_2, \; P_A, \; P_B$ , then
$P_A \; - \; P_2 \; = \; P_B \; - \; P_A$

c. d. is the common difference

$P_{1806} - P_2 = P_{2554} - P_{1806}$
$4891551 - 5 = 9783097 - 4891551 = 4891546$

$P_{2083930} - P_2 = P_{2947122} - P_{2083930}$
$= 6514145325385 - 5 = 13028290650765 - 6514145325385 = 6514145325380$

$P_{2404853222} - P_2 = P_{3400976042} - P_{2404853222}$
$= 8674978527843245315 - 5$
$= 17349957055686490625 - 8674978527843245315$
$= 8674978527843245310$

$P_{2775198534066} - P_2 = P_{3924723405154} - P_{2775198534066}$
$= 11552590355221725444471501 - 5$
$= 23105180710443450888942997 - 11552590355221725444471501$
$= 11552590355221725444471496$

$P_{3202576703458750} - P_2 = P_{4529127408571482} - P_{3202576703458750}$
$P_{3202576703458750} = 15384746312305069900031075614375$
$P_{4529127408571482} = 30769492624610139800062151228745$
c. d. = $15384746312305069900031075614370$

$P_{3695770740592863242} - P_2 = P_{5226609104768084882} - P_{3695770740592863242}$
$P_{5226609104768084882} = 20488082050533481266494762105275694225$
$P_{5226609104768084882} = 40976164101066962532989524210551388445$
c. d. = $20488082050533481266494762105275694220$

$P_{4264916232067460722326} - P_2 = P_{6031502377774961382154} - P_{4264916232067460722326}$
$P_{4264916232067460722326} = 27284265699828759725016500552365084781914251$
$P_{6031502377774961382154} = 54568531399657519450033001104730169563828497$
c. d. = $27284265699828759725016500552365084781914246$

$P_{4921709636035109080700770} - P_2 = P_{6960348517343200666920642} - P_{4921709636035109080700770}$
$P_{4921709636035109080700770} = 36334838612161268846390090535325821753156877538965$
$P_{6960348517343200666920642} = 72669677224322537692780181070651643506313755077925$
c. d. = $36334838612161268846390090535325821753156877538960$

$P_{5679648655068283811667966062} - P_2$
$= P_{8032236157511675794665038522} - P_{5679648655068283811667966062}$
$P_{5679648655068283811667966062} = 48387613267528447714801704267435874889631192930141698735$
$P_{8032236157511675794665038522} = 96775226535056895429603408534871749779262385860283397465$
c. d. = $48387613267528447714801704267435874889631192930141698730$

$P_{6554309626239163483555752134586} - P_2$
$= P_{9269193565419956523842787533554} - P_{6554309626239163483555752134586}$
$P_{6554309626239163483555752134586} = 64438462014917044381457275527957708602234988640017565310019801$
$P_{9269193565419956523842787533554} = 128876924029834088762914551055915417204469977280035130620039597$
c. d. = $64438462014917044381457275527957708602234988640017565310019796$

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math grad - Interest: Number theory

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