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Home/Chain Registry/Block #3,008,425

Block #3,008,425

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/13/2019, 10:20:45 PM Β· Difficulty 11.2024 Β· 3,833,994 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fcca9f5329f8772e86183957aef2501b4ffd2133e82e879c0bd70eaed3432553
View on Chainz β†—

Difficulty

11.202356

Transactions

1

Size

200 B

Version

2

Bits

0b33cd9a

Nonce

60,735,235

Timestamp

1/13/2019, 10:20:45 PM

Confirmations

3,833,994

Merkle Root

474073edb254c6b2b4e1f1e470bd5a4e7578be88e9f8e7ff90e0298e0a1f92d9
Transactions (1)
Coinbase474073edb254c6…e0298e0a1f92d9
1 in β†’ 1 out7.9600 XPM110 B
AUhjokok…k5m93PZR
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.

1.676 Γ— 10⁹⁴(95-digit number)
16769122450213398966…35520728873241480000
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
1.676 Γ— 10⁹⁴(95-digit number)
16769122450213398966…35520728873241479999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.676 Γ— 10⁹⁴(95-digit number)
16769122450213398966…35520728873241480001
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
3.353 Γ— 10⁹⁴(95-digit number)
33538244900426797933…71041457746482959999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.353 Γ— 10⁹⁴(95-digit number)
33538244900426797933…71041457746482960001
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
6.707 Γ— 10⁹⁴(95-digit number)
67076489800853595867…42082915492965919999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.707 Γ— 10⁹⁴(95-digit number)
67076489800853595867…42082915492965920001
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
1.341 Γ— 10⁹⁡(96-digit number)
13415297960170719173…84165830985931839999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.341 Γ— 10⁹⁡(96-digit number)
13415297960170719173…84165830985931840001
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
2.683 Γ— 10⁹⁡(96-digit number)
26830595920341438347…68331661971863679999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.683 Γ— 10⁹⁡(96-digit number)
26830595920341438347…68331661971863680001
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
5.366 Γ— 10⁹⁡(96-digit number)
53661191840682876694…36663323943727359999
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 3008425

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 fcca9f5329f8772e86183957aef2501b4ffd2133e82e879c0bd70eaed3432553

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 #3,008,425 on Chainz β†—
Circulating Supply:57,983,766 XPMΒ·at block #6,842,418 Β· updates every 60s
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