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Home/Chain Registry/Block #2,144,044

Block #2,144,044

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/3/2017, 7:06:57 PM Β· Difficulty 10.8833 Β· 4,688,679 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4475f511b68e5d45c8a3a1f401123f15b0b4ca7d20ea3c1f4926c8e5e7182cd5
View on Chainz β†—

Difficulty

10.883269

Transactions

1

Size

199 B

Version

2

Bits

0ae21de4

Nonce

1,092,433,062

Timestamp

6/3/2017, 7:06:57 PM

Confirmations

4,688,679

Merkle Root

ab1c90da72a441d4bfd36391eda2a1d7938d965354f00031da945d01c5b516ff
Transactions (1)
Coinbaseab1c90da72a441…945d01c5b516ff
1 in β†’ 1 out8.4300 XPM109 B
APMjLF1F…VWKpqruS
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.

3.544 Γ— 10⁹³(94-digit number)
35443056374023635254…45042173105786950400
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
3.544 Γ— 10⁹³(94-digit number)
35443056374023635254…45042173105786950399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.544 Γ— 10⁹³(94-digit number)
35443056374023635254…45042173105786950401
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
7.088 Γ— 10⁹³(94-digit number)
70886112748047270509…90084346211573900799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.088 Γ— 10⁹³(94-digit number)
70886112748047270509…90084346211573900801
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
1.417 Γ— 10⁹⁴(95-digit number)
14177222549609454101…80168692423147801599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.417 Γ— 10⁹⁴(95-digit number)
14177222549609454101…80168692423147801601
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
2.835 Γ— 10⁹⁴(95-digit number)
28354445099218908203…60337384846295603199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.835 Γ— 10⁹⁴(95-digit number)
28354445099218908203…60337384846295603201
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
5.670 Γ— 10⁹⁴(95-digit number)
56708890198437816407…20674769692591206399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.670 Γ— 10⁹⁴(95-digit number)
56708890198437816407…20674769692591206401
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 2144044

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 4475f511b68e5d45c8a3a1f401123f15b0b4ca7d20ea3c1f4926c8e5e7182cd5

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 #2,144,044 on Chainz β†—
Circulating Supply:57,905,941 XPMΒ·at block #6,832,722 Β· updates every 60s
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