The minimum percentage of common stock held by investors for not exercise of warrants.

No definition available.

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Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

The amount of proceeds from exercise of warrants in exchange for issuance of pre-funded warrants.

+ References

No definition available.

+ Details

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Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

The maximum number of shares permitted to be issued by an entity's charter and bylaws.

+ References

No definition available.

+ Details

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Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

Number of warrants exercised during the current period.

+ References

No definition available.

+ Details

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Namespace Prefix:	ptgx_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Date the warrants or rights are exercisable, in YYYY-MM-DD format.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 505
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481112/505-10-50-3

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:dateItemType
Balance Type:	na
Period Type:	duration

- Definition

Exercise price per share or per unit of warrants or rights outstanding.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S50
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480738/235-10-S50-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.4-08(h)(4))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480678/235-10-S99-1

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 505
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481112/505-10-50-3

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	instant

- Definition

Number of securities into which the class of warrant or right may be converted. For example, but not limited to, 500,000 warrants may be converted into 1,000,000 shares.

+ References

+ Details

Name:	us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

The maximum number of common shares permitted to be issued by an entity's charter and bylaws.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(29))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.6-04(16)(a))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479170/946-210-S99-1

+ Details

Name:	us-gaap_CommonStockSharesAuthorized
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

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

- Details

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Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_StatementEquityComponentsAxis=us-gaap_CommonStockMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_SubsidiarySaleOfStockAxis=us-gaap_PrivatePlacementMember
Namespace Prefix:
Data Type:	na
Balance Type:
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Stockholders' Equity (Details) - USD ($) $ / shares in Units, $ in Millions	1 Months Ended	3 Months Ended	6 Months Ended
	Aug. 31, 2023	Jun. 30, 2024	Jun. 30, 2024	Jun. 30, 2025	Dec. 31, 2024	Jun. 20, 2024	Jun. 19, 2024	Aug. 31, 2018
Stockholders' Equity
Common Stock, Shares Authorized				180,000,000	180,000,000	180,000,000	90,000,000
Shares authorized						190,000,000	100,000,000
Warrants issued to purchase common stock, number of shares	2,705,252			1,500,000
Exercise Price (per share)	$ 0.001
Proceeds from exercise of Warrants in exchange for issuance of Pre-Funded Warrants	$ 34.4
Number of shares issued upon exercise of warrants	44,748		84,992
Minimum percentage of common stock held by investors for not exercise of warrants	9.99%
Investors
Stockholders' Equity
Warrants exercisable date	Aug. 08, 2023
Common Stock
Stockholders' Equity
Warrants issued to purchase common stock, number of shares				0
Number of shares issued upon exercise of warrants		84,989	84,989
Common Stock \| Investors \| Private Placement
Stockholders' Equity
Warrants issued to purchase common stock, number of shares								2,750,000