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Block #382,822

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/31/2014, 12:14:57 AM Β· Difficulty 10.3994 Β· 6,444,109 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1f86dc10ff9e48d6618400baa8d5c23b7701c54fee2a57a78dd857eb9ec070b4
View on Chainz β†—

Height

#382,822

Difficulty

10.399353

Transactions

1

Size

202 B

Version

2

Bits

0a663c01

Nonce

934,345

Timestamp

1/31/2014, 12:14:57 AM

Confirmations

6,444,109

Merkle Root

dd4f3c009e07b6a165ecd8453e218b51148843a6b2eae15b2df4639a930077b4
Transactions (1)
Coinbasedd4f3c009e07b6…f4639a930077b4
1 in β†’ 1 out9.2300 XPM110 B
AeKNrjNj…1NEq95Ta
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.

2.242 Γ— 10⁹⁸(99-digit number)
22422687072747710492…68462650756904763520
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
2.242 Γ— 10⁹⁸(99-digit number)
22422687072747710492…68462650756904763519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.242 Γ— 10⁹⁸(99-digit number)
22422687072747710492…68462650756904763521
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
4.484 Γ— 10⁹⁸(99-digit number)
44845374145495420985…36925301513809527039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.484 Γ— 10⁹⁸(99-digit number)
44845374145495420985…36925301513809527041
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
8.969 Γ— 10⁹⁸(99-digit number)
89690748290990841970…73850603027619054079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.969 Γ— 10⁹⁸(99-digit number)
89690748290990841970…73850603027619054081
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
1.793 Γ— 10⁹⁹(100-digit number)
17938149658198168394…47701206055238108159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.793 Γ— 10⁹⁹(100-digit number)
17938149658198168394…47701206055238108161
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
3.587 Γ— 10⁹⁹(100-digit number)
35876299316396336788…95402412110476216319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.587 Γ— 10⁹⁹(100-digit number)
35876299316396336788…95402412110476216321
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 382822

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 1f86dc10ff9e48d6618400baa8d5c23b7701c54fee2a57a78dd857eb9ec070b4

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 #382,822 on Chainz β†—
Circulating Supply:57,859,620 XPMΒ·at block #6,826,930 Β· updates every 60s
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