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Home/Chain Registry/Block #2,631,668

Block #2,631,668

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/27/2018, 7:01:15 AM Β· Difficulty 11.1743 Β· 4,213,055 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b817a265c14c35adf7c8464684a5127cd210342b7ee8eec98067e92a0a424d44
View on Chainz β†—

Difficulty

11.174333

Transactions

2

Size

426 B

Version

2

Bits

0b2ca110

Nonce

274,352,446

Timestamp

4/27/2018, 7:01:15 AM

Confirmations

4,213,055

Merkle Root

a04cfa541b26a12fc8a61ed5a0e61dee60d5afc925f1d3c509945afdaa7aca43
Transactions (2)
Coinbasee5fce0d17ba9a5…a32c54ffeaeeb4
1 in β†’ 1 out8.0100 XPM110 B
AJogz8hb…tQ8nvLqN
471230b7d8ccb3…b7868080bf0583
1 in β†’ 2 out6712.6542 XPM225 B
AGNLBHS1…6gZzB1VuARTGxeAc…WmRAvHDa
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.

5.792 Γ— 10⁹⁢(97-digit number)
57924479675229456920…77653915261159600000
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
5.792 Γ— 10⁹⁢(97-digit number)
57924479675229456920…77653915261159599999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.792 Γ— 10⁹⁢(97-digit number)
57924479675229456920…77653915261159600001
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
1.158 Γ— 10⁹⁷(98-digit number)
11584895935045891384…55307830522319199999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.158 Γ— 10⁹⁷(98-digit number)
11584895935045891384…55307830522319200001
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
2.316 Γ— 10⁹⁷(98-digit number)
23169791870091782768…10615661044638399999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.316 Γ— 10⁹⁷(98-digit number)
23169791870091782768…10615661044638400001
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
4.633 Γ— 10⁹⁷(98-digit number)
46339583740183565536…21231322089276799999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.633 Γ— 10⁹⁷(98-digit number)
46339583740183565536…21231322089276800001
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
9.267 Γ— 10⁹⁷(98-digit number)
92679167480367131073…42462644178553599999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.267 Γ— 10⁹⁷(98-digit number)
92679167480367131073…42462644178553600001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.853 Γ— 10⁹⁸(99-digit number)
18535833496073426214…84925288357107199999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2631668

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 b817a265c14c35adf7c8464684a5127cd210342b7ee8eec98067e92a0a424d44

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 #2,631,668 on Chainz β†—
Circulating Supply:58,002,195 XPMΒ·at block #6,844,722 Β· updates every 60s
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