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Block #392,032

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/6/2014, 5:25:29 AM Β· Difficulty 10.4326 Β· 6,411,943 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7f13077124c9be9e212558d093a708ef609aae56d02bf71f38837fb67fe1c993
View on Chainz β†—

Height

#392,032

Difficulty

10.432620

Transactions

1

Size

199 B

Version

2

Bits

0a6ec035

Nonce

112,214

Timestamp

2/6/2014, 5:25:29 AM

Confirmations

6,411,943

Merkle Root

ed5ba6032134987077449cb4396fa3c07f53bc50f2c6aa37a71143f7993233e2
Transactions (1)
Coinbaseed5ba603213498…1143f7993233e2
1 in β†’ 1 out9.1700 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.

1.292 Γ— 10⁹³(94-digit number)
12920881149304981288…01159081564961952160
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
1.292 Γ— 10⁹³(94-digit number)
12920881149304981288…01159081564961952159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.292 Γ— 10⁹³(94-digit number)
12920881149304981288…01159081564961952161
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
2.584 Γ— 10⁹³(94-digit number)
25841762298609962576…02318163129923904319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.584 Γ— 10⁹³(94-digit number)
25841762298609962576…02318163129923904321
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
5.168 Γ— 10⁹³(94-digit number)
51683524597219925152…04636326259847808639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.168 Γ— 10⁹³(94-digit number)
51683524597219925152…04636326259847808641
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
1.033 Γ— 10⁹⁴(95-digit number)
10336704919443985030…09272652519695617279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.033 Γ— 10⁹⁴(95-digit number)
10336704919443985030…09272652519695617281
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
2.067 Γ— 10⁹⁴(95-digit number)
20673409838887970061…18545305039391234559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.067 Γ— 10⁹⁴(95-digit number)
20673409838887970061…18545305039391234561
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 392032

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 7f13077124c9be9e212558d093a708ef609aae56d02bf71f38837fb67fe1c993

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 #392,032 on Chainz β†—
Circulating Supply:57,675,847 XPMΒ·at block #6,803,974 Β· updates every 60s
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