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Block #337,117

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/31/2013, 10:41:15 AM Β· Difficulty 10.1408 Β· 6,463,189 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
c8298c9739bc24c6caebf7901eb075d66fc6719a00062d45c66f20924b2d4c83
View on Chainz β†—

Height

#337,117

Difficulty

10.140800

Transactions

2

Size

394 B

Version

2

Bits

0a240b78

Nonce

51,339

Timestamp

12/31/2013, 10:41:15 AM

Confirmations

6,463,189

Merkle Root

2ffbcc110ade99d3452748669f84874f10a773eb230199564c09d81bf4815149
Transactions (2)
Coinbase976b96a43f919c…e2bda397de2132
1 in β†’ 1 out9.7202 XPM110 B
AeKNrjNj…1NEq95Ta
c5d6e5c51eb44d…ef3b3e157ca6e2
1 in β†’ 1 out0.9900 XPM193 B
AVT5gBoU…wqoTSRTA
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.197 Γ— 10⁹⁢(97-digit number)
11974080656586243119…47544570106833148000
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
1.197 Γ— 10⁹⁢(97-digit number)
11974080656586243119…47544570106833147999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.197 Γ— 10⁹⁢(97-digit number)
11974080656586243119…47544570106833148001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
2.394 Γ— 10⁹⁢(97-digit number)
23948161313172486238…95089140213666295999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.394 Γ— 10⁹⁢(97-digit number)
23948161313172486238…95089140213666296001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
4.789 Γ— 10⁹⁢(97-digit number)
47896322626344972476…90178280427332591999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.789 Γ— 10⁹⁢(97-digit number)
47896322626344972476…90178280427332592001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
9.579 Γ— 10⁹⁢(97-digit number)
95792645252689944952…80356560854665183999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.579 Γ— 10⁹⁢(97-digit number)
95792645252689944952…80356560854665184001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
1.915 Γ— 10⁹⁷(98-digit number)
19158529050537988990…60713121709330367999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.915 Γ— 10⁹⁷(98-digit number)
19158529050537988990…60713121709330368001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10
How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 337117

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock c8298c9739bc24c6caebf7901eb075d66fc6719a00062d45c66f20924b2d4c83

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #337,117 on Chainz β†—
Circulating Supply:57,646,511 XPMΒ·at block #6,800,305 Β· updates every 60s
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