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Block #382,461

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/30/2014, 5:48:24 PM Β· Difficulty 10.4034 Β· 6,443,788 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1d7a802feb683d53b35c42130e4e40583bc3ab95e565a6433612aebae39f0cc8
View on Chainz β†—

Height

#382,461

Difficulty

10.403406

Transactions

1

Size

199 B

Version

2

Bits

0a6745a5

Nonce

173,639

Timestamp

1/30/2014, 5:48:24 PM

Confirmations

6,443,788

Merkle Root

71322d0398b33bc8284b5e34d885c9d26d49dcde0e3923cf93dbb229935899f1
Transactions (1)
Coinbase71322d0398b33b…dbb229935899f1
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.

9.926 Γ— 10⁹¹(92-digit number)
99264517968512739650…64915900611231724160
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
9.926 Γ— 10⁹¹(92-digit number)
99264517968512739650…64915900611231724159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.926 Γ— 10⁹¹(92-digit number)
99264517968512739650…64915900611231724161
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
1.985 Γ— 10⁹²(93-digit number)
19852903593702547930…29831801222463448319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.985 Γ— 10⁹²(93-digit number)
19852903593702547930…29831801222463448321
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
3.970 Γ— 10⁹²(93-digit number)
39705807187405095860…59663602444926896639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.970 Γ— 10⁹²(93-digit number)
39705807187405095860…59663602444926896641
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
7.941 Γ— 10⁹²(93-digit number)
79411614374810191720…19327204889853793279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.941 Γ— 10⁹²(93-digit number)
79411614374810191720…19327204889853793281
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
1.588 Γ— 10⁹³(94-digit number)
15882322874962038344…38654409779707586559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.588 Γ— 10⁹³(94-digit number)
15882322874962038344…38654409779707586561
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 382461

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 1d7a802feb683d53b35c42130e4e40583bc3ab95e565a6433612aebae39f0cc8

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 #382,461 on Chainz β†—
Circulating Supply:57,854,125 XPMΒ·at block #6,826,248 Β· updates every 60s
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