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Home/Chain Registry/Block #2,083,017

Block #2,083,017

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/22/2017, 5:09:44 PM Β· Difficulty 10.8706 Β· 4,759,287 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9497f05c8d4bb32c1d45b00f579c2b0f9321303c8ed4776fef2b71fb4e72c7b2
View on Chainz β†—

Difficulty

10.870566

Transactions

1

Size

200 B

Version

2

Bits

0adedd6c

Nonce

383,328,474

Timestamp

4/22/2017, 5:09:44 PM

Confirmations

4,759,287

Merkle Root

56ea283027f98ef1e080f1d9fd84da9c676c282d032ed7f4f0898f53ac74a444
Transactions (1)
Coinbase56ea283027f98e…898f53ac74a444
1 in β†’ 1 out8.4500 XPM110 B
AR2Ao3Yi…Wt14A8wV
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.

4.049 Γ— 10⁹⁴(95-digit number)
40490830618661655057…43156319997943851420
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
4.049 Γ— 10⁹⁴(95-digit number)
40490830618661655057…43156319997943851419
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.049 Γ— 10⁹⁴(95-digit number)
40490830618661655057…43156319997943851421
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
8.098 Γ— 10⁹⁴(95-digit number)
80981661237323310115…86312639995887702839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.098 Γ— 10⁹⁴(95-digit number)
80981661237323310115…86312639995887702841
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
1.619 Γ— 10⁹⁡(96-digit number)
16196332247464662023…72625279991775405679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.619 Γ— 10⁹⁡(96-digit number)
16196332247464662023…72625279991775405681
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
3.239 Γ— 10⁹⁡(96-digit number)
32392664494929324046…45250559983550811359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.239 Γ— 10⁹⁡(96-digit number)
32392664494929324046…45250559983550811361
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
6.478 Γ— 10⁹⁡(96-digit number)
64785328989858648092…90501119967101622719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.478 Γ— 10⁹⁡(96-digit number)
64785328989858648092…90501119967101622721
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2083017

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 9497f05c8d4bb32c1d45b00f579c2b0f9321303c8ed4776fef2b71fb4e72c7b2

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 #2,083,017 on Chainz β†—
Circulating Supply:57,982,837 XPMΒ·at block #6,842,303 Β· updates every 60s
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