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Block #51,337

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/16/2013, 5:21:07 AM Β· Difficulty 8.8969 Β· 6,754,470 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2eda09a99ac239f7d7243694890d2ed13884fa0682f9232e73fd289034812f72
View on Chainz β†—

Height

#51,337

Difficulty

8.896918

Transactions

1

Size

203 B

Version

2

Bits

08e59c70

Nonce

1,020

Timestamp

7/16/2013, 5:21:07 AM

Confirmations

6,754,470

Merkle Root

406e06b1491093387ba13e1fd3e0d8dbbce3e705a312f4f55498aba95f500232
Transactions (1)
Coinbase406e06b1491093…98aba95f500232
1 in β†’ 1 out12.6200 XPM109 B
AKsLKPc8…zkBgUqcr
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.

2.363 Γ— 10¹⁰⁡(106-digit number)
23633178429660446520…81559616879288816260
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
2.363 Γ— 10¹⁰⁡(106-digit number)
23633178429660446520…81559616879288816259
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.363 Γ— 10¹⁰⁡(106-digit number)
23633178429660446520…81559616879288816261
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
4.726 Γ— 10¹⁰⁡(106-digit number)
47266356859320893041…63119233758577632519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.726 Γ— 10¹⁰⁡(106-digit number)
47266356859320893041…63119233758577632521
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
9.453 Γ— 10¹⁰⁡(106-digit number)
94532713718641786083…26238467517155265039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.453 Γ— 10¹⁰⁡(106-digit number)
94532713718641786083…26238467517155265041
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
1.890 Γ— 10¹⁰⁢(107-digit number)
18906542743728357216…52476935034310530079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.890 Γ— 10¹⁰⁢(107-digit number)
18906542743728357216…52476935034310530081
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8
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 51337

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 2eda09a99ac239f7d7243694890d2ed13884fa0682f9232e73fd289034812f72

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 #51,337 on Chainz β†—
Circulating Supply:57,690,541 XPMΒ·at block #6,805,806 Β· updates every 60s
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