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Home/Chain Registry/Block #2,084,949

Block #2,084,949

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/23/2017, 11:54:02 PM Β· Difficulty 10.8728 Β· 4,757,400 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3ab15891c2bb1e31fb5482104eea575795b499d9303bf750d7e2f9a88c22694d
View on Chainz β†—

Difficulty

10.872796

Transactions

1

Size

200 B

Version

2

Bits

0adf6f94

Nonce

359,600,203

Timestamp

4/23/2017, 11:54:02 PM

Confirmations

4,757,400

Merkle Root

60d6e4cf0805fde37e8c038ce27f2b3402cbca760a83e53c25c7ff2c45378bb5
Transactions (1)
Coinbase60d6e4cf0805fd…c7ff2c45378bb5
1 in β†’ 1 out8.4500 XPM110 B
AevxCDek…u6bNpT9s
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.

5.546 Γ— 10⁹⁡(96-digit number)
55461967184325654394…72851577496528773120
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
5.546 Γ— 10⁹⁡(96-digit number)
55461967184325654394…72851577496528773119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.546 Γ— 10⁹⁡(96-digit number)
55461967184325654394…72851577496528773121
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
1.109 Γ— 10⁹⁢(97-digit number)
11092393436865130878…45703154993057546239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.109 Γ— 10⁹⁢(97-digit number)
11092393436865130878…45703154993057546241
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
2.218 Γ— 10⁹⁢(97-digit number)
22184786873730261757…91406309986115092479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.218 Γ— 10⁹⁢(97-digit number)
22184786873730261757…91406309986115092481
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
4.436 Γ— 10⁹⁢(97-digit number)
44369573747460523515…82812619972230184959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.436 Γ— 10⁹⁢(97-digit number)
44369573747460523515…82812619972230184961
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
8.873 Γ— 10⁹⁢(97-digit number)
88739147494921047031…65625239944460369919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.873 Γ— 10⁹⁢(97-digit number)
88739147494921047031…65625239944460369921
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 2084949

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 3ab15891c2bb1e31fb5482104eea575795b499d9303bf750d7e2f9a88c22694d

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 #2,084,949 on Chainz β†—
Circulating Supply:57,983,198 XPMΒ·at block #6,842,348 Β· updates every 60s
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