<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2003-12-26</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><issuer><issuerCik>0000318107</issuerCik><issuerName>PRIMA ENERGY CORP</issuerName>        <issuerTradingSymbol>PENG</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001228526</rptOwnerCik><rptOwnerName>LEWIS RICHARD H</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>1099 18TH STREET</rptOwnerStreet1><rptOwnerStreet2>SUITE 400</rptOwnerStreet2><rptOwnerCity>DENVER</rptOwnerCity><rptOwnerState>CO</rptOwnerState><rptOwnerZipCode>80202-1908</rptOwnerZipCode><rptOwnerStateDescription></rptOwnerStateDescription></reportingOwnerAddress><reportingOwnerRelationship><isDirector>1</isDirector><isOfficer>1</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther><officerTitle>President</officerTitle></reportingOwnerRelationship></reportingOwner><nonDerivativeTable><nonDerivativeHolding><securityTitle><value>Common stock</value></securityTitle><postTransactionAmounts><sharesOwnedFollowingTransaction><value>23281.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>I</value></directOrIndirectOwnership><natureOfOwnership><value>ESOP Trust</value></natureOfOwnership></ownershipNature></nonDerivativeHolding><nonDerivativeHolding><securityTitle><value>Common stock</value></securityTitle><postTransactionAmounts><sharesOwnedFollowingTransaction><value>112500.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>I</value></directOrIndirectOwnership><natureOfOwnership><value>by Spouse</value></natureOfOwnership></ownershipNature></nonDerivativeHolding><nonDerivativeHolding><securityTitle><value>Common stock</value></securityTitle><postTransactionAmounts><sharesOwnedFollowingTransaction><value>5730.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>I</value></directOrIndirectOwnership><natureOfOwnership><value>by Children</value></natureOfOwnership></ownershipNature></nonDerivativeHolding><nonDerivativeTransaction><securityTitle><value>Common stock</value></securityTitle><transactionDate><value>2003-12-29</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>S</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>5000.0000</value></transactionShares><transactionPricePerShare><value>34.4800</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>180027.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>I</value></directOrIndirectOwnership><natureOfOwnership><value>by Family Limited Partnership</value></natureOfOwnership></ownershipNature></nonDerivativeTransaction><nonDerivativeTransaction><securityTitle><value>Common stock</value></securityTitle><transactionDate><value>2003-12-26</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>S</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>2165.0000</value></transactionShares><transactionPricePerShare><value>34.2500</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>1057788.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction></nonDerivativeTable><derivativeTable><derivativeHolding><securityTitle><value>Stock options</value></securityTitle><conversionOrExercisePrice><value>4.4100</value></conversionOrExercisePrice><exerciseDate><footnoteId id="F1" /></exerciseDate><expirationDate><value>2005-05-21</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>168750.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>168750.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeHolding><derivativeHolding><securityTitle><value>Stock options</value></securityTitle><conversionOrExercisePrice><value>6.6700</value></conversionOrExercisePrice><exerciseDate><footnoteId id="F1" /></exerciseDate><expirationDate><value>2008-09-17</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>225000.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>225000.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeHolding><derivativeHolding><securityTitle><value>Stock options</value></securityTitle><conversionOrExercisePrice><value>33.2500</value></conversionOrExercisePrice><exerciseDate><footnoteId id="F1" /></exerciseDate><expirationDate><value>2011-03-11</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>100000.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>100000.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeHolding><derivativeHolding><securityTitle><value>Stock options</value></securityTitle><conversionOrExercisePrice><value>26.3800</value></conversionOrExercisePrice><exerciseDate><footnoteId id="F1" /></exerciseDate><expirationDate><value>2012-03-18</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>25000.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>25000.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeHolding><derivativeHolding><securityTitle><value>Stock options</value></securityTitle><conversionOrExercisePrice><value>20.1900</value></conversionOrExercisePrice><exerciseDate><footnoteId id="F1" /></exerciseDate><expirationDate><value>2013-05-12</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>7500.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>7500.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeHolding><derivativeHolding><securityTitle><value>Stock options</value></securityTitle><conversionOrExercisePrice><value>23.0400</value></conversionOrExercisePrice><exerciseDate><footnoteId id="F1" /></exerciseDate><expirationDate><value>2013-08-11</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>7500.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>7500.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeHolding></derivativeTable><footnotes><footnote id="F1">Stock options vest 20% per year over five years.</footnote></footnotes><remarks></remarks><ownerSignature><signatureName>Richard H. Lewis</signatureName><signatureDate>2003-12-30</signatureDate></ownerSignature></ownershipDocument>

