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Home/Chain Registry/Block #1,371,624

Block #1,371,624

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/16/2015, 3:11:08 PM Β· Difficulty 10.8108 Β· 5,444,405 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c398e7b0a35dee55a260d5ceb9083a55cd00fa0597b856a8c2c104b01b3238c9
View on Chainz β†—

Difficulty

10.810755

Transactions

1

Size

200 B

Version

2

Bits

0acf8da5

Nonce

1,283,120,572

Timestamp

12/16/2015, 3:11:08 PM

Confirmations

5,444,405

Merkle Root

3d662536e24067306f3af9db1eb6629ffd8413f278336bf2d2238bff9b6ba269
Transactions (1)
Coinbase3d662536e24067…238bff9b6ba269
1 in β†’ 1 out8.5400 XPM110 B
AG1pkVax…HSth6jTp
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.

7.551 Γ— 10⁹³(94-digit number)
75515765773673104067…33598011007650586000
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
7.551 Γ— 10⁹³(94-digit number)
75515765773673104067…33598011007650585999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.551 Γ— 10⁹³(94-digit number)
75515765773673104067…33598011007650586001
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
1.510 Γ— 10⁹⁴(95-digit number)
15103153154734620813…67196022015301171999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.510 Γ— 10⁹⁴(95-digit number)
15103153154734620813…67196022015301172001
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
3.020 Γ— 10⁹⁴(95-digit number)
30206306309469241627…34392044030602343999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.020 Γ— 10⁹⁴(95-digit number)
30206306309469241627…34392044030602344001
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
6.041 Γ— 10⁹⁴(95-digit number)
60412612618938483254…68784088061204687999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.041 Γ— 10⁹⁴(95-digit number)
60412612618938483254…68784088061204688001
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
1.208 Γ— 10⁹⁡(96-digit number)
12082522523787696650…37568176122409375999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.208 Γ— 10⁹⁡(96-digit number)
12082522523787696650…37568176122409376001
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 1371624

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 c398e7b0a35dee55a260d5ceb9083a55cd00fa0597b856a8c2c104b01b3238c9

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 #1,371,624 on Chainz β†—
Circulating Supply:57,772,345 XPMΒ·at block #6,816,028 Β· updates every 60s
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