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Block #509,404

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/25/2014, 12:41:12 AM Β· Difficulty 10.8206 Β· 6,291,676 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
aa375a43fe30746071cc598ad912d0ae9d36d60f5eca3bf636f5b2964f41e4cf
View on Chainz β†—

Height

#509,404

Difficulty

10.820609

Transactions

1

Size

244 B

Version

2

Bits

0ad2136d

Nonce

100,135,580

Timestamp

4/25/2014, 12:41:12 AM

Confirmations

6,291,676

Merkle Root

e452da9bf01453be50c998464aa896486657c7c229573faa0290c01693a1f57a
Transactions (1)
Coinbasee452da9bf01453…90c01693a1f57a
1 in β†’ 2 out8.5300 XPM152 B
AdorbYVE…PXEXPtczALPu3s2c…EJXLjVFh
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.

6.240 Γ— 10⁹⁸(99-digit number)
62407420272766791281…60097123359275302760
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
6.240 Γ— 10⁹⁸(99-digit number)
62407420272766791281…60097123359275302759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.240 Γ— 10⁹⁸(99-digit number)
62407420272766791281…60097123359275302761
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
1.248 Γ— 10⁹⁹(100-digit number)
12481484054553358256…20194246718550605519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.248 Γ— 10⁹⁹(100-digit number)
12481484054553358256…20194246718550605521
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
2.496 Γ— 10⁹⁹(100-digit number)
24962968109106716512…40388493437101211039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.496 Γ— 10⁹⁹(100-digit number)
24962968109106716512…40388493437101211041
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
4.992 Γ— 10⁹⁹(100-digit number)
49925936218213433025…80776986874202422079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.992 Γ— 10⁹⁹(100-digit number)
49925936218213433025…80776986874202422081
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
9.985 Γ— 10⁹⁹(100-digit number)
99851872436426866050…61553973748404844159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.985 Γ— 10⁹⁹(100-digit number)
99851872436426866050…61553973748404844161
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 509404

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 aa375a43fe30746071cc598ad912d0ae9d36d60f5eca3bf636f5b2964f41e4cf

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 #509,404 on Chainz β†—
Circulating Supply:57,652,703 XPMΒ·at block #6,801,079 Β· updates every 60s
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