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Home/Chain Registry/Block #1,967,893

Block #1,967,893

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/3/2017, 10:39:42 PM Β· Difficulty 10.7524 Β· 4,872,123 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7e72e104c6e776a72c0e617947d46505bfb6f3d3fc255039914911388fb8c6cc
View on Chainz β†—

Difficulty

10.752386

Transactions

1

Size

201 B

Version

2

Bits

0ac09c66

Nonce

156,241,805

Timestamp

2/3/2017, 10:39:42 PM

Confirmations

4,872,123

Merkle Root

87bf8e66ad620dcf136a873ef4531bfb3d815549c5f5de136cbf71364f927d02
Transactions (1)
Coinbase87bf8e66ad620d…bf71364f927d02
1 in β†’ 1 out8.6400 XPM110 B
AVumL6gi…Jo2nDwB5
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.

3.101 Γ— 10⁹⁢(97-digit number)
31011461429986087515…51417341868577259520
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
3.101 Γ— 10⁹⁢(97-digit number)
31011461429986087515…51417341868577259519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.101 Γ— 10⁹⁢(97-digit number)
31011461429986087515…51417341868577259521
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
6.202 Γ— 10⁹⁢(97-digit number)
62022922859972175030…02834683737154519039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.202 Γ— 10⁹⁢(97-digit number)
62022922859972175030…02834683737154519041
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
1.240 Γ— 10⁹⁷(98-digit number)
12404584571994435006…05669367474309038079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.240 Γ— 10⁹⁷(98-digit number)
12404584571994435006…05669367474309038081
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
2.480 Γ— 10⁹⁷(98-digit number)
24809169143988870012…11338734948618076159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.480 Γ— 10⁹⁷(98-digit number)
24809169143988870012…11338734948618076161
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
4.961 Γ— 10⁹⁷(98-digit number)
49618338287977740024…22677469897236152319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.961 Γ— 10⁹⁷(98-digit number)
49618338287977740024…22677469897236152321
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 1967893

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 7e72e104c6e776a72c0e617947d46505bfb6f3d3fc255039914911388fb8c6cc

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 #1,967,893 on Chainz β†—
Circulating Supply:57,964,441 XPMΒ·at block #6,840,015 Β· updates every 60s
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