XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,843,353

Block #2,843,353

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/17/2018, 12:24:21 PM Β· Difficulty 11.7256 Β· 4,000,557 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
aa521ef560077fe84711f14cf9314c434cad19dc3801a961ca970be093b57cc6
View on Chainz β†—

Difficulty

11.725596

Transactions

1

Size

200 B

Version

2

Bits

0bb9c0aa

Nonce

1,565,663,873

Timestamp

9/17/2018, 12:24:21 PM

Confirmations

4,000,557

Merkle Root

a2804e0e8c5fd64f0ddb69d4f90fff51420326f3647fb85d6606d07af53d9e11
Transactions (1)
Coinbasea2804e0e8c5fd6…06d07af53d9e11
1 in β†’ 1 out7.2600 XPM110 B
AWAjttTD…4fUVZnxn
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.

3.511 Γ— 10⁹⁡(96-digit number)
35112392059049175188…13836520142417220480
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
3.511 Γ— 10⁹⁡(96-digit number)
35112392059049175188…13836520142417220479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.511 Γ— 10⁹⁡(96-digit number)
35112392059049175188…13836520142417220481
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
7.022 Γ— 10⁹⁡(96-digit number)
70224784118098350376…27673040284834440959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.022 Γ— 10⁹⁡(96-digit number)
70224784118098350376…27673040284834440961
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
1.404 Γ— 10⁹⁢(97-digit number)
14044956823619670075…55346080569668881919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.404 Γ— 10⁹⁢(97-digit number)
14044956823619670075…55346080569668881921
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
2.808 Γ— 10⁹⁢(97-digit number)
28089913647239340150…10692161139337763839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.808 Γ— 10⁹⁢(97-digit number)
28089913647239340150…10692161139337763841
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
5.617 Γ— 10⁹⁢(97-digit number)
56179827294478680301…21384322278675527679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.617 Γ— 10⁹⁢(97-digit number)
56179827294478680301…21384322278675527681
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
1.123 Γ— 10⁹⁷(98-digit number)
11235965458895736060…42768644557351055359
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 2843353

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 aa521ef560077fe84711f14cf9314c434cad19dc3801a961ca970be093b57cc6

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 #2,843,353 on Chainz β†—
Circulating Supply:57,995,650 XPMΒ·at block #6,843,909 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy