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Home/Chain Registry/Block #2,633,244

Block #2,633,244

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/28/2018, 8:30:32 AM Β· Difficulty 11.1820 Β· 4,208,843 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9c2f2f9a7886ae94f23784e665d719f9e3758b8cc7768782bd4e2a76ebad6b95
View on Chainz β†—

Difficulty

11.181981

Transactions

1

Size

201 B

Version

2

Bits

0b2e9655

Nonce

496,208,932

Timestamp

4/28/2018, 8:30:32 AM

Confirmations

4,208,843

Merkle Root

300af3cbd3595e9f1a7cbd38284459f90a569b53333439e8a1079f6b80cfabef
Transactions (1)
Coinbase300af3cbd3595e…079f6b80cfabef
1 in β†’ 1 out7.9800 XPM110 B
Adqah8zh…1WwoHJ9t
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.

1.098 Γ— 10⁹⁷(98-digit number)
10987176241130285784…91340255720040529920
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
1.098 Γ— 10⁹⁷(98-digit number)
10987176241130285784…91340255720040529919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.098 Γ— 10⁹⁷(98-digit number)
10987176241130285784…91340255720040529921
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
2.197 Γ— 10⁹⁷(98-digit number)
21974352482260571568…82680511440081059839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.197 Γ— 10⁹⁷(98-digit number)
21974352482260571568…82680511440081059841
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
4.394 Γ— 10⁹⁷(98-digit number)
43948704964521143136…65361022880162119679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.394 Γ— 10⁹⁷(98-digit number)
43948704964521143136…65361022880162119681
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
8.789 Γ— 10⁹⁷(98-digit number)
87897409929042286273…30722045760324239359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.789 Γ— 10⁹⁷(98-digit number)
87897409929042286273…30722045760324239361
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
1.757 Γ— 10⁹⁸(99-digit number)
17579481985808457254…61444091520648478719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.757 Γ— 10⁹⁸(99-digit number)
17579481985808457254…61444091520648478721
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
3.515 Γ— 10⁹⁸(99-digit number)
35158963971616914509…22888183041296957439
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 2633244

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 9c2f2f9a7886ae94f23784e665d719f9e3758b8cc7768782bd4e2a76ebad6b95

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 #2,633,244 on Chainz β†—
Circulating Supply:57,981,081 XPMΒ·at block #6,842,086 Β· updates every 60s
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