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Home/Chain Registry/Block #2,843,204

Block #2,843,204

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/17/2018, 9:59:05 AM Β· Difficulty 11.7254 Β· 3,990,658 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0430071f80a2b10269081abf7bdb415194f7a8facbdf14faa600558b3923d9ec
View on Chainz β†—

Difficulty

11.725437

Transactions

2

Size

1016 B

Version

2

Bits

0bb9b645

Nonce

161,403,751

Timestamp

9/17/2018, 9:59:05 AM

Confirmations

3,990,658

Merkle Root

79886d1c98b1beec43833d704aa7e92ab576d88d8fb34dd6c0941e4337f2e781
Transactions (2)
Coinbase94ac3bc568da8f…6e7f84c15a91f9
1 in β†’ 1 out7.2700 XPM110 B
AZcaZeup…ebMnPTKh
eb92dfc5efffa6…73f108097a96b8
5 in β†’ 2 out256.8336 XPM816 B
AY8PErqK…gv7kMfQzAXHEEN53…Mdnjow2R
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.

7.984 Γ— 10⁹⁴(95-digit number)
79848006427116987218…67648329027206694000
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
7.984 Γ— 10⁹⁴(95-digit number)
79848006427116987218…67648329027206693999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.984 Γ— 10⁹⁴(95-digit number)
79848006427116987218…67648329027206694001
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
1.596 Γ— 10⁹⁡(96-digit number)
15969601285423397443…35296658054413387999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.596 Γ— 10⁹⁡(96-digit number)
15969601285423397443…35296658054413388001
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
3.193 Γ— 10⁹⁡(96-digit number)
31939202570846794887…70593316108826775999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.193 Γ— 10⁹⁡(96-digit number)
31939202570846794887…70593316108826776001
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
6.387 Γ— 10⁹⁡(96-digit number)
63878405141693589774…41186632217653551999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.387 Γ— 10⁹⁡(96-digit number)
63878405141693589774…41186632217653552001
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
1.277 Γ— 10⁹⁢(97-digit number)
12775681028338717954…82373264435307103999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.277 Γ— 10⁹⁢(97-digit number)
12775681028338717954…82373264435307104001
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
2.555 Γ— 10⁹⁢(97-digit number)
25551362056677435909…64746528870614207999
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 2843204

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 0430071f80a2b10269081abf7bdb415194f7a8facbdf14faa600558b3923d9ec

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 #2,843,204 on Chainz β†—
Circulating Supply:57,915,126 XPMΒ·at block #6,833,861 Β· updates every 60s
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