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Home/Chain Registry/Block #2,266,055

Block #2,266,055

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/24/2017, 4:09:10 PM Β· Difficulty 10.9514 Β· 4,575,259 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e7eeb66770e82b50a7e12f74ee0695d93e186a0eb2fe54a3ca71c24ab913bfea
View on Chainz β†—

Difficulty

10.951428

Transactions

3

Size

1.36 KB

Version

2

Bits

0af390cb

Nonce

320,659,954

Timestamp

8/24/2017, 4:09:10 PM

Confirmations

4,575,259

Merkle Root

6b24f9c1ba9aa5588e036cb30c019c5d7d1dbb6226880d535f02d5d6c0b3d603
Transactions (3)
Coinbase9d881cb3ff5296…7bd66d80d2fc72
1 in β†’ 1 out8.3400 XPM110 B
AWdhiqGL…9ZYLhGux
21001173a85520…9f9b3a89d073c9
1 in β†’ 2 out97.2800 XPM227 B
AGg6ghUz…dMz6irvVAdWvKcP1…78PdzeKw
c1fa2a5c34c78c…5eb3f7eaef8dee
6 in β†’ 2 out60.4600 XPM966 B
AcpYzhW7…xBAQBNdQAMdM8iRk…LPWU55c7
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.

1.236 Γ— 10⁹⁴(95-digit number)
12362755248481881212…84470363173440412160
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
1.236 Γ— 10⁹⁴(95-digit number)
12362755248481881212…84470363173440412159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.236 Γ— 10⁹⁴(95-digit number)
12362755248481881212…84470363173440412161
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
2.472 Γ— 10⁹⁴(95-digit number)
24725510496963762424…68940726346880824319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.472 Γ— 10⁹⁴(95-digit number)
24725510496963762424…68940726346880824321
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
4.945 Γ— 10⁹⁴(95-digit number)
49451020993927524849…37881452693761648639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.945 Γ— 10⁹⁴(95-digit number)
49451020993927524849…37881452693761648641
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
9.890 Γ— 10⁹⁴(95-digit number)
98902041987855049699…75762905387523297279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.890 Γ— 10⁹⁴(95-digit number)
98902041987855049699…75762905387523297281
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
1.978 Γ— 10⁹⁡(96-digit number)
19780408397571009939…51525810775046594559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.978 Γ— 10⁹⁡(96-digit number)
19780408397571009939…51525810775046594561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2266055

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 e7eeb66770e82b50a7e12f74ee0695d93e186a0eb2fe54a3ca71c24ab913bfea

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 #2,266,055 on Chainz β†—
Circulating Supply:57,974,874 XPMΒ·at block #6,841,313 Β· updates every 60s
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