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Home/Chain Registry/Block #2,643,256

Block #2,643,256

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/2/2018, 1:07:10 AM Β· Difficulty 11.6779 Β· 4,187,411 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d46a25bb6d10aba421f1bf97e815bde09c4c7184ea513a8fa5daa56e4d0addb2
View on Chainz β†—

Difficulty

11.677944

Transactions

1

Size

199 B

Version

2

Bits

0bad8dc4

Nonce

1,124,597,592

Timestamp

5/2/2018, 1:07:10 AM

Confirmations

4,187,411

Merkle Root

2c86cea214febf61dfccc4b23313a8a2043d694f6d4c4e67b05654c67517afbc
Transactions (1)
Coinbase2c86cea214febf…5654c67517afbc
1 in β†’ 1 out7.3200 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.

5.717 Γ— 10⁹²(93-digit number)
57175164432997912355…42410497053862191040
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
5.717 Γ— 10⁹²(93-digit number)
57175164432997912355…42410497053862191039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.717 Γ— 10⁹²(93-digit number)
57175164432997912355…42410497053862191041
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
1.143 Γ— 10⁹³(94-digit number)
11435032886599582471…84820994107724382079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.143 Γ— 10⁹³(94-digit number)
11435032886599582471…84820994107724382081
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
2.287 Γ— 10⁹³(94-digit number)
22870065773199164942…69641988215448764159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.287 Γ— 10⁹³(94-digit number)
22870065773199164942…69641988215448764161
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
4.574 Γ— 10⁹³(94-digit number)
45740131546398329884…39283976430897528319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.574 Γ— 10⁹³(94-digit number)
45740131546398329884…39283976430897528321
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
9.148 Γ— 10⁹³(94-digit number)
91480263092796659768…78567952861795056639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.148 Γ— 10⁹³(94-digit number)
91480263092796659768…78567952861795056641
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
1.829 Γ— 10⁹⁴(95-digit number)
18296052618559331953…57135905723590113279
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 2643256

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 d46a25bb6d10aba421f1bf97e815bde09c4c7184ea513a8fa5daa56e4d0addb2

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 #2,643,256 on Chainz β†—
Circulating Supply:57,889,464 XPMΒ·at block #6,830,666 Β· updates every 60s
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