XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,822,910

Block #2,822,910

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/3/2018, 1:59:16 PM Β· Difficulty 11.7035 Β· 4,019,590 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
bed71da7944cd67666d6d1f03f425d279413bfa257b5c4fb9beb36de92a3ee79
View on Chainz β†—

Difficulty

11.703532

Transactions

1

Size

199 B

Version

2

Bits

0bb41aab

Nonce

360,785,199

Timestamp

9/3/2018, 1:59:16 PM

Confirmations

4,019,590

Merkle Root

d9bc6a52748d9bd7bdf36420650e78543516381eb8b5f74db7b1933b401e7731
Transactions (1)
Coinbased9bc6a52748d9b…b1933b401e7731
1 in β†’ 1 out7.2900 XPM109 B
AaYyCqeM…pcsmwHNZ
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.

4.607 Γ— 10⁹⁡(96-digit number)
46077802868170849348…08792342244555297120
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
4.607 Γ— 10⁹⁡(96-digit number)
46077802868170849348…08792342244555297119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.607 Γ— 10⁹⁡(96-digit number)
46077802868170849348…08792342244555297121
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
9.215 Γ— 10⁹⁡(96-digit number)
92155605736341698696…17584684489110594239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.215 Γ— 10⁹⁡(96-digit number)
92155605736341698696…17584684489110594241
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
1.843 Γ— 10⁹⁢(97-digit number)
18431121147268339739…35169368978221188479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.843 Γ— 10⁹⁢(97-digit number)
18431121147268339739…35169368978221188481
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
3.686 Γ— 10⁹⁢(97-digit number)
36862242294536679478…70338737956442376959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.686 Γ— 10⁹⁢(97-digit number)
36862242294536679478…70338737956442376961
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
7.372 Γ— 10⁹⁢(97-digit number)
73724484589073358957…40677475912884753919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.372 Γ— 10⁹⁢(97-digit number)
73724484589073358957…40677475912884753921
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
1.474 Γ— 10⁹⁷(98-digit number)
14744896917814671791…81354951825769507839
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 2822910

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 bed71da7944cd67666d6d1f03f425d279413bfa257b5c4fb9beb36de92a3ee79

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 #2,822,910 on Chainz β†—
Circulating Supply:57,984,419 XPMΒ·at block #6,842,499 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