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Home/Chain Registry/Block #1,441,008

Block #1,441,008

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/3/2016, 3:00:10 PM Β· Difficulty 10.7643 Β· 5,401,287 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
02b4c46c3ab20c8920ab95c8994c706023898454a8b0dca90f64589d17520f9b
View on Chainz β†—

Difficulty

10.764321

Transactions

1

Size

242 B

Version

2

Bits

0ac3aa89

Nonce

1,124,624,122

Timestamp

2/3/2016, 3:00:10 PM

Confirmations

5,401,287

Merkle Root

efe0029618db2f34f6e0013f18847293ea65a3923443add04362e19ba04cea77
Transactions (1)
Coinbaseefe0029618db2f…62e19ba04cea77
1 in β†’ 2 out8.6200 XPM152 B
AbNVgXWJ…g3uNfMnjALPu3s2c…EJXLjVFh
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.

2.331 Γ— 10⁹⁡(96-digit number)
23312681851030829941…96949171614224106160
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
2.331 Γ— 10⁹⁡(96-digit number)
23312681851030829941…96949171614224106159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.331 Γ— 10⁹⁡(96-digit number)
23312681851030829941…96949171614224106161
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
4.662 Γ— 10⁹⁡(96-digit number)
46625363702061659883…93898343228448212319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.662 Γ— 10⁹⁡(96-digit number)
46625363702061659883…93898343228448212321
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
9.325 Γ— 10⁹⁡(96-digit number)
93250727404123319766…87796686456896424639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.325 Γ— 10⁹⁡(96-digit number)
93250727404123319766…87796686456896424641
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
1.865 Γ— 10⁹⁢(97-digit number)
18650145480824663953…75593372913792849279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.865 Γ— 10⁹⁢(97-digit number)
18650145480824663953…75593372913792849281
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
3.730 Γ— 10⁹⁢(97-digit number)
37300290961649327906…51186745827585698559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.730 Γ— 10⁹⁢(97-digit number)
37300290961649327906…51186745827585698561
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 1441008

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 02b4c46c3ab20c8920ab95c8994c706023898454a8b0dca90f64589d17520f9b

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 #1,441,008 on Chainz β†—
Circulating Supply:57,982,763 XPMΒ·at block #6,842,294 Β· updates every 60s
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