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Home/Chain Registry/Block #2,641,622

Block #2,641,622

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/1/2018, 10:24:51 AM Β· Difficulty 11.6261 Β· 4,189,518 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8547396e0860d541dd2ad139d95e770d52a656e9903bf2d60e05910535c1f137
View on Chainz β†—

Difficulty

11.626147

Transactions

1

Size

200 B

Version

2

Bits

0ba04b2a

Nonce

1,093,151,570

Timestamp

5/1/2018, 10:24:51 AM

Confirmations

4,189,518

Merkle Root

489aa225bf8425b8bbd47f147f2416b07df73a461749e91a3560a45e4b929a3b
Transactions (1)
Coinbase489aa225bf8425…60a45e4b929a3b
1 in β†’ 1 out7.3900 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.

4.294 Γ— 10⁹⁴(95-digit number)
42943231914233135742…21604865338072518640
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
4.294 Γ— 10⁹⁴(95-digit number)
42943231914233135742…21604865338072518639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.294 Γ— 10⁹⁴(95-digit number)
42943231914233135742…21604865338072518641
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
8.588 Γ— 10⁹⁴(95-digit number)
85886463828466271484…43209730676145037279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.588 Γ— 10⁹⁴(95-digit number)
85886463828466271484…43209730676145037281
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
1.717 Γ— 10⁹⁡(96-digit number)
17177292765693254296…86419461352290074559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.717 Γ— 10⁹⁡(96-digit number)
17177292765693254296…86419461352290074561
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
3.435 Γ— 10⁹⁡(96-digit number)
34354585531386508593…72838922704580149119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.435 Γ— 10⁹⁡(96-digit number)
34354585531386508593…72838922704580149121
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
6.870 Γ— 10⁹⁡(96-digit number)
68709171062773017187…45677845409160298239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.870 Γ— 10⁹⁡(96-digit number)
68709171062773017187…45677845409160298241
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
1.374 Γ— 10⁹⁢(97-digit number)
13741834212554603437…91355690818320596479
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 2641622

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 8547396e0860d541dd2ad139d95e770d52a656e9903bf2d60e05910535c1f137

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 #2,641,622 on Chainz β†—
Circulating Supply:57,893,267 XPMΒ·at block #6,831,139 Β· updates every 60s
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