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Home/Chain Registry/Block #2,812,022

Block #2,812,022

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/27/2018, 9:47:32 AM Β· Difficulty 11.6686 Β· 4,031,083 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b6814ec34a60866cdbd4020b435f0a50a53253016050d43001ffb6cc672fbfb4
View on Chainz β†—

Difficulty

11.668551

Transactions

1

Size

201 B

Version

2

Bits

0bab2629

Nonce

269,677,669

Timestamp

8/27/2018, 9:47:32 AM

Confirmations

4,031,083

Merkle Root

b51f316c645e7b722a9444500f0419bbd300eb71565a10b52cc2e08ef6014369
Transactions (1)
Coinbaseb51f316c645e7b…c2e08ef6014369
1 in β†’ 1 out7.3300 XPM109 B
AdQr6Y1m…LSSgbyJG
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.

1.066 Γ— 10⁹⁹(100-digit number)
10660438322426124422…03323769527606886400
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
1.066 Γ— 10⁹⁹(100-digit number)
10660438322426124422…03323769527606886399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.066 Γ— 10⁹⁹(100-digit number)
10660438322426124422…03323769527606886401
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
2.132 Γ— 10⁹⁹(100-digit number)
21320876644852248844…06647539055213772799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.132 Γ— 10⁹⁹(100-digit number)
21320876644852248844…06647539055213772801
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
4.264 Γ— 10⁹⁹(100-digit number)
42641753289704497689…13295078110427545599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.264 Γ— 10⁹⁹(100-digit number)
42641753289704497689…13295078110427545601
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
8.528 Γ— 10⁹⁹(100-digit number)
85283506579408995378…26590156220855091199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.528 Γ— 10⁹⁹(100-digit number)
85283506579408995378…26590156220855091201
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
1.705 Γ— 10¹⁰⁰(101-digit number)
17056701315881799075…53180312441710182399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.705 Γ— 10¹⁰⁰(101-digit number)
17056701315881799075…53180312441710182401
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
3.411 Γ— 10¹⁰⁰(101-digit number)
34113402631763598151…06360624883420364799
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 2812022

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 b6814ec34a60866cdbd4020b435f0a50a53253016050d43001ffb6cc672fbfb4

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 #2,812,022 on Chainz β†—
Circulating Supply:57,989,204 XPMΒ·at block #6,843,104 Β· updates every 60s
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