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Home/Chain Registry/Block #2,812,803

Block #2,812,803

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/27/2018, 9:36:51 PM Β· Difficulty 11.6732 Β· 4,020,315 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d71df8c17dbfad490e271e2f5d47458a04c0d615b99c4d874cce0992bd488dd1
View on Chainz β†—

Difficulty

11.673215

Transactions

1

Size

201 B

Version

2

Bits

0bac57cf

Nonce

1,922,880,606

Timestamp

8/27/2018, 9:36:51 PM

Confirmations

4,020,315

Merkle Root

6b86a199e9ea6825be51193ee2ce322f18fe33d6a851a8ff783ff728d8168b1f
Transactions (1)
Coinbase6b86a199e9ea68…3ff728d8168b1f
1 in β†’ 1 out7.3300 XPM110 B
AZtxQr2F…7grUWrUz
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.

3.094 Γ— 10⁹⁷(98-digit number)
30945610577081728638…29293458228242841600
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
3.094 Γ— 10⁹⁷(98-digit number)
30945610577081728638…29293458228242841599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.094 Γ— 10⁹⁷(98-digit number)
30945610577081728638…29293458228242841601
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
6.189 Γ— 10⁹⁷(98-digit number)
61891221154163457276…58586916456485683199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.189 Γ— 10⁹⁷(98-digit number)
61891221154163457276…58586916456485683201
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
1.237 Γ— 10⁹⁸(99-digit number)
12378244230832691455…17173832912971366399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.237 Γ— 10⁹⁸(99-digit number)
12378244230832691455…17173832912971366401
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
2.475 Γ— 10⁹⁸(99-digit number)
24756488461665382910…34347665825942732799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.475 Γ— 10⁹⁸(99-digit number)
24756488461665382910…34347665825942732801
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
4.951 Γ— 10⁹⁸(99-digit number)
49512976923330765821…68695331651885465599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.951 Γ— 10⁹⁸(99-digit number)
49512976923330765821…68695331651885465601
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
9.902 Γ— 10⁹⁸(99-digit number)
99025953846661531642…37390663303770931199
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 2812803

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 d71df8c17dbfad490e271e2f5d47458a04c0d615b99c4d874cce0992bd488dd1

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 #2,812,803 on Chainz β†—
Circulating Supply:57,909,120 XPMΒ·at block #6,833,117 Β· updates every 60s
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