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Leases - Summary of Operating Leases of Lessee (Detail) - USD ($) $ in Thousands	Sep. 30, 2025	Dec. 31, 2024
Leases [Abstract]
Gross carrying amount beginning of year	$ 21,903	$ 23,398
Increased asset from new leases	452	3,066
Accumulated amortization	(2,203)	(4,561)
Net book value	20,152	21,903
Lease liabilities	$ 21,221	$ 22,941

X

- Definition

Accumulated amortization operating lease right of use asset.

+ References

No definition available.

+ Details

Name:	bprn_AccumulatedAmortizationOperatingLeaseRightOfUseAsset
Namespace Prefix:	bprn_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

X

- Definition

Gross carrying amount operating lease right of use asset.

+ References

No definition available.

+ Details

Name:	bprn_GrossCarryingAmountOperatingLeaseRightOfUseAsset
Namespace Prefix:	bprn_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

X

- Definition

New lease operating lease right of use asset.

+ References

No definition available.

+ Details

Name:	bprn_NewLeaseOperatingLeaseRightOfUseAsset
Namespace Prefix:	bprn_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

X

- References

No definition available.

+ Details

Name:	us-gaap_LeasesAbstract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Present value of lessee's discounted obligation for lease payments from operating lease.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479041/842-20-45-1

+ Details

Name:	us-gaap_OperatingLeaseLiability
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

X

- Definition

Amount of lessee's right to use underlying asset under operating lease.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479041/842-20-45-1

+ Details

Name:	us-gaap_OperatingLeaseRightOfUseAsset
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant