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  <xs:element id="prme_ChangeInFairValueOfShortTermInvestment" abstract="false" name="ChangeInFairValueOfShortTermInvestment" nillable="true" xbrli:periodType="duration" xbrli:balance="credit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="prme_SharesIssuedSharesShareBasedPaymentArrangementESPPAfterForfeiture" abstract="false" name="SharesIssuedSharesShareBasedPaymentArrangementESPPAfterForfeiture" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="xbrli:sharesItemType"/>
  <xs:element id="prme_AccretionAmortizationOfDiscountsAndPremiumsShortTermInvestments" abstract="false" name="AccretionAmortizationOfDiscountsAndPremiumsShortTermInvestments" nillable="true" xbrli:periodType="duration" xbrli:balance="credit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="prme_IncreaseDecreaseInAccruedSettlementPayment" abstract="false" name="IncreaseDecreaseInAccruedSettlementPayment" nillable="true" xbrli:periodType="duration" xbrli:balance="debit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="prme_PaymentsForSecurityDeposits" abstract="false" name="PaymentsForSecurityDeposits" nillable="true" xbrli:periodType="duration" xbrli:balance="credit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="prme_ProceedsFromIssuanceFollowOnOffering" abstract="false" name="ProceedsFromIssuanceFollowOnOffering" nillable="true" xbrli:periodType="duration" xbrli:balance="debit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="prme_ProceedsFromResearchAndDevelopmentFundingLiability" abstract="false" name="ProceedsFromResearchAndDevelopmentFundingLiability" nillable="true" xbrli:periodType="duration" xbrli:balance="debit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="prme_ProceedsFromESPPOfferings" abstract="false" name="ProceedsFromESPPOfferings" nillable="true" xbrli:periodType="duration" xbrli:balance="debit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="prme_PublicOfferingMember" abstract="true" name="PublicOfferingMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="prme_WarrantsPolicyTextBlock" abstract="false" name="WarrantsPolicyTextBlock" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:textBlockItemType"/>
  <xs:element id="prme_OrganizationConsolidationAndPresentationOfFinancialStatementsTable" abstract="true" name="OrganizationConsolidationAndPresentationOfFinancialStatementsTable" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrldt:hypercubeItem" type="xbrli:stringItemType"/>
  <xs:element id="prme_WarrantPurchaseAgreementMember" abstract="true" name="WarrantPurchaseAgreementMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="prme_OrganizationConsolidationAndPresentationOfFinancialStatementsLineItems" abstract="true" name="OrganizationConsolidationAndPresentationOfFinancialStatementsLineItems" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="xbrli:stringItemType"/>
  <xs:element id="prme_USTreasuryBillsAndGovernmentSecuritiesMember" abstract="true" name="USTreasuryBillsAndGovernmentSecuritiesMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types1:domainItemType"/>
  <xs:element id="prme_LaboratoryEquipmentMember" abstract="true" name="LaboratoryEquipmentMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types1:domainItemType"/>
  <xs:element id="prme_AccruedLabRelatedSuppliesAndServicesCurrent" abstract="false" name="AccruedLabRelatedSuppliesAndServicesCurrent" nillable="true" xbrli:periodType="instant" xbrli:balance="credit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="prme_A60FirstStreetCambridgeMassachusettsLeaseMember" abstract="true" name="A60FirstStreetCambridgeMassachusettsLeaseMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types1:domainItemType"/>
  <xs:element id="prme_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" abstract="false" name="LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" nillable="true" xbrli:periodType="instant" xbrli:balance="credit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="prme_SalesAgreementMember" abstract="true" name="SalesAgreementMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="prme_CommonStockParOrStatedValuePerShareUnderAmendment" abstract="false" name="CommonStockParOrStatedValuePerShareUnderAmendment" nillable="true" xbrli:periodType="instant" substitutionGroup="xbrli:item" type="dtr-types:perShareItemType"/>
  <xs:element id="prme_CommonStockNumberOfVotesPerShare" abstract="false" name="CommonStockNumberOfVotesPerShare" nillable="true" xbrli:periodType="instant" substitutionGroup="xbrli:item" type="xbrli:integerItemType"/>
  <xs:element id="prme_TimeBasedStockOptionsMember" abstract="true" name="TimeBasedStockOptionsMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types1:domainItemType"/>
  <xs:element id="prme_PerformanceBasedStockOptionsMember" abstract="true" name="PerformanceBasedStockOptionsMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types1:domainItemType"/>
  <xs:element id="prme_RestrictedStockTimeBasedMember" abstract="true" name="RestrictedStockTimeBasedMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types1:domainItemType"/>
  <xs:element id="prme_RestrictedStockPerformanceBasedMember" abstract="true" name="RestrictedStockPerformanceBasedMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types1:domainItemType"/>
  <xs:element id="prme_A2022StockOptionAndIncentivePlanMember" abstract="true" name="A2022StockOptionAndIncentivePlanMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types1:domainItemType"/>
  <xs:element id="prme_A2022StockOptionAndIncentivePlanAnd2019EquityIncentivePlanMember" abstract="true" name="A2022StockOptionAndIncentivePlanAnd2019EquityIncentivePlanMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types1:domainItemType"/>
  <xs:element id="prme_A2022EmployeeStockPurchasePlanMember" abstract="true" name="A2022EmployeeStockPurchasePlanMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types1:domainItemType"/>
  <xs:element id="prme_ShareBasedCompensationArrangementByShareBasedPaymentAwardAnnualIncreaseInSharesReservedForIssuancePercentage" abstract="false" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardAnnualIncreaseInSharesReservedForIssuancePercentage" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types1:percentItemType"/>
  <xs:element id="prme_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfAdditionalSharesAllowableUnderThePlan" abstract="false" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfAdditionalSharesAllowableUnderThePlan" nillable="true" xbrli:periodType="instant" substitutionGroup="xbrli:item" type="xbrli:sharesItemType"/>
  <xs:element id="prme_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsWeightedAverageGrantDateFairValueAbstract" abstract="true" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsWeightedAverageGrantDateFairValueAbstract" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="xbrli:stringItemType"/>
  <xs:element id="prme_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageGrantDateFairValue" abstract="false" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageGrantDateFairValue" nillable="true" xbrli:periodType="instant" substitutionGroup="xbrli:item" type="dtr-types1:perShareItemType"/>
  <xs:element id="prme_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageGrantDateFairValue" abstract="false" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageGrantDateFairValue" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types1:perShareItemType"/>
  <xs:element id="prme_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresWeightedAverageGrantDateFairValue" abstract="false" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresWeightedAverageGrantDateFairValue" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types1:perShareItemType"/>
  <xs:element id="prme_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageGrantDateFairValueNumber" abstract="false" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageGrantDateFairValueNumber" nillable="true" xbrli:periodType="instant" substitutionGroup="xbrli:item" type="dtr-types1:perShareItemType"/>
  <xs:element id="prme_CoFounderShareholderMember" abstract="true" name="CoFounderShareholderMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types1:domainItemType"/>
  <xs:element id="prme_MyeloidTherapeuticsMember" abstract="true" name="MyeloidTherapeuticsMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types1:domainItemType"/>
  <xs:element id="prme_JeffreyMarrazzoMember" abstract="true" name="JeffreyMarrazzoMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="prme_ScientificConsultingMember" abstract="true" name="ScientificConsultingMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types1:domainItemType"/>
  <xs:element id="prme_AdvisoryServicesAgreementMember" abstract="true" name="AdvisoryServicesAgreementMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="prme_SettlementPaymentExpense" abstract="false" name="SettlementPaymentExpense" nillable="true" xbrli:periodType="duration" xbrli:balance="debit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="prme_SaleOfStockNumberOfSharesIssuedInTransactionGrantDateFairValue" abstract="false" name="SaleOfStockNumberOfSharesIssuedInTransactionGrantDateFairValue" nillable="true" xbrli:periodType="instant" xbrli:balance="credit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
</xs:schema>
