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Home/Chain Registry/Block #1,691,292

Block #1,691,292

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/27/2016, 12:22:21 PM Β· Difficulty 10.6892 Β· 5,139,702 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
cfde2b456cfb7003f7d2c76cfaec06e55b2aa9896c58aa2566115fc3fb5b5263
View on Chainz β†—

Difficulty

10.689169

Transactions

1

Size

200 B

Version

2

Bits

0ab06d63

Nonce

612,007,050

Timestamp

7/27/2016, 12:22:21 PM

Confirmations

5,139,702

Merkle Root

0724e93f454f2f72be1c7485935955b76b9cb3e2e1eee3cfdb94bdec0918d179
Transactions (1)
Coinbase0724e93f454f2f…94bdec0918d179
1 in β†’ 1 out8.7400 XPM110 B
AWjCBYhf…TZTB6dfP
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.

1.814 Γ— 10⁹⁴(95-digit number)
18148098200650615254…90246825882149504000
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
1.814 Γ— 10⁹⁴(95-digit number)
18148098200650615254…90246825882149503999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.814 Γ— 10⁹⁴(95-digit number)
18148098200650615254…90246825882149504001
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
3.629 Γ— 10⁹⁴(95-digit number)
36296196401301230509…80493651764299007999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.629 Γ— 10⁹⁴(95-digit number)
36296196401301230509…80493651764299008001
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
7.259 Γ— 10⁹⁴(95-digit number)
72592392802602461019…60987303528598015999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.259 Γ— 10⁹⁴(95-digit number)
72592392802602461019…60987303528598016001
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
1.451 Γ— 10⁹⁡(96-digit number)
14518478560520492203…21974607057196031999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.451 Γ— 10⁹⁡(96-digit number)
14518478560520492203…21974607057196032001
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
2.903 Γ— 10⁹⁡(96-digit number)
29036957121040984407…43949214114392063999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.903 Γ— 10⁹⁡(96-digit number)
29036957121040984407…43949214114392064001
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 1691292

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 cfde2b456cfb7003f7d2c76cfaec06e55b2aa9896c58aa2566115fc3fb5b5263

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 #1,691,292 on Chainz β†—
Circulating Supply:57,892,093 XPMΒ·at block #6,830,993 Β· updates every 60s
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