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Home/Chain Registry/Block #2,665,433

Block #2,665,433

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/17/2018, 3:15:01 PM Β· Difficulty 11.6613 Β· 4,178,368 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1a3d42b6346bce4bc5fcd0e35dd3f7e7b6ed05318faef0692582a3537ec9d3e4
View on Chainz β†—

Difficulty

11.661328

Transactions

2

Size

2.01 KB

Version

2

Bits

0ba94cce

Nonce

642,783,173

Timestamp

5/17/2018, 3:15:01 PM

Confirmations

4,178,368

Merkle Root

e5617ed188fd032e48bd92bedbeed7db718d02aa886fc374f292a35fdc84418b
Transactions (2)
Coinbase16497b000d4ae0…c260c7d7855f27
1 in β†’ 1 out7.3600 XPM110 B
AV4kTU7B…7HwamcEk
dbd218b6b7b2d0…86c5d1170a56c5
12 in β†’ 2 out10450.0100 XPM1.81 KB
ALYrJi2G…zT8PFjQuAY7135hn…za27BqGa
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.

3.841 Γ— 10⁹⁢(97-digit number)
38414061129934340473…33785489162685153280
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
3.841 Γ— 10⁹⁢(97-digit number)
38414061129934340473…33785489162685153279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.841 Γ— 10⁹⁢(97-digit number)
38414061129934340473…33785489162685153281
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
7.682 Γ— 10⁹⁢(97-digit number)
76828122259868680946…67570978325370306559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.682 Γ— 10⁹⁢(97-digit number)
76828122259868680946…67570978325370306561
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
1.536 Γ— 10⁹⁷(98-digit number)
15365624451973736189…35141956650740613119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.536 Γ— 10⁹⁷(98-digit number)
15365624451973736189…35141956650740613121
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
3.073 Γ— 10⁹⁷(98-digit number)
30731248903947472378…70283913301481226239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.073 Γ— 10⁹⁷(98-digit number)
30731248903947472378…70283913301481226241
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
6.146 Γ— 10⁹⁷(98-digit number)
61462497807894944757…40567826602962452479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.146 Γ— 10⁹⁷(98-digit number)
61462497807894944757…40567826602962452481
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
1.229 Γ— 10⁹⁸(99-digit number)
12292499561578988951…81135653205924904959
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 2665433

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 1a3d42b6346bce4bc5fcd0e35dd3f7e7b6ed05318faef0692582a3537ec9d3e4

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 #2,665,433 on Chainz β†—
Circulating Supply:57,994,785 XPMΒ·at block #6,843,800 Β· updates every 60s
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