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Home/Chain Registry/Block #2,845,287

Block #2,845,287

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/18/2018, 7:49:24 PM Β· Difficulty 11.7283 Β· 4,000,362 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1186843933247cd25d904e068b064f9e8c0b929b0e9b0ad83df7dbac5305f824
View on Chainz β†—

Difficulty

11.728308

Transactions

1

Size

201 B

Version

2

Bits

0bba7264

Nonce

837,456,736

Timestamp

9/18/2018, 7:49:24 PM

Confirmations

4,000,362

Merkle Root

265ad1e67b4b4d7905d18ce8ae746f39ec63de9865c85e0be0c577c5cca4ba06
Transactions (1)
Coinbase265ad1e67b4b4d…c577c5cca4ba06
1 in β†’ 1 out7.2600 XPM110 B
AaLxrXY4…gFUrmfNR
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.

1.344 Γ— 10⁹⁢(97-digit number)
13447754912409484303…35785476243346698240
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
1.344 Γ— 10⁹⁢(97-digit number)
13447754912409484303…35785476243346698239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.344 Γ— 10⁹⁢(97-digit number)
13447754912409484303…35785476243346698241
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
2.689 Γ— 10⁹⁢(97-digit number)
26895509824818968606…71570952486693396479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.689 Γ— 10⁹⁢(97-digit number)
26895509824818968606…71570952486693396481
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
5.379 Γ— 10⁹⁢(97-digit number)
53791019649637937212…43141904973386792959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.379 Γ— 10⁹⁢(97-digit number)
53791019649637937212…43141904973386792961
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
1.075 Γ— 10⁹⁷(98-digit number)
10758203929927587442…86283809946773585919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.075 Γ— 10⁹⁷(98-digit number)
10758203929927587442…86283809946773585921
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
2.151 Γ— 10⁹⁷(98-digit number)
21516407859855174885…72567619893547171839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.151 Γ— 10⁹⁷(98-digit number)
21516407859855174885…72567619893547171841
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
4.303 Γ— 10⁹⁷(98-digit number)
43032815719710349770…45135239787094343679
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 2845287

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 1186843933247cd25d904e068b064f9e8c0b929b0e9b0ad83df7dbac5305f824

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 #2,845,287 on Chainz β†—
Circulating Supply:58,009,641 XPMΒ·at block #6,845,648 Β· updates every 60s
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