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Home/Chain Registry/Block #2,644,522

Block #2,644,522

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/2/2018, 1:07:02 PM Β· Difficulty 11.7111 Β· 4,186,558 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
225e04baf5e835199cbab40f1a81a8652196d9ec9a34a888274e327846ef733e
View on Chainz β†—

Difficulty

11.711057

Transactions

1

Size

200 B

Version

2

Bits

0bb607cd

Nonce

128,181,377

Timestamp

5/2/2018, 1:07:02 PM

Confirmations

4,186,558

Merkle Root

9c13a2e46575dac6381f183a6e38bf9c8e0f711d3ac2d1a0d573611787a4ca7e
Transactions (1)
Coinbase9c13a2e46575da…73611787a4ca7e
1 in β†’ 1 out7.2800 XPM110 B
AdPHuqF5…F2CPSvAz
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.

9.636 Γ— 10⁹⁴(95-digit number)
96360978243249969099…20751925487715332000
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
9.636 Γ— 10⁹⁴(95-digit number)
96360978243249969099…20751925487715331999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.636 Γ— 10⁹⁴(95-digit number)
96360978243249969099…20751925487715332001
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
1.927 Γ— 10⁹⁡(96-digit number)
19272195648649993819…41503850975430663999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.927 Γ— 10⁹⁡(96-digit number)
19272195648649993819…41503850975430664001
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
3.854 Γ— 10⁹⁡(96-digit number)
38544391297299987639…83007701950861327999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.854 Γ— 10⁹⁡(96-digit number)
38544391297299987639…83007701950861328001
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
7.708 Γ— 10⁹⁡(96-digit number)
77088782594599975279…66015403901722655999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.708 Γ— 10⁹⁡(96-digit number)
77088782594599975279…66015403901722656001
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
1.541 Γ— 10⁹⁢(97-digit number)
15417756518919995055…32030807803445311999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.541 Γ— 10⁹⁢(97-digit number)
15417756518919995055…32030807803445312001
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
3.083 Γ— 10⁹⁢(97-digit number)
30835513037839990111…64061615606890623999
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 2644522

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 225e04baf5e835199cbab40f1a81a8652196d9ec9a34a888274e327846ef733e

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 #2,644,522 on Chainz β†—
Circulating Supply:57,892,781 XPMΒ·at block #6,831,079 Β· updates every 60s
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