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Home/Chain Registry/Block #3,082,328

Block #3,082,328

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/7/2019, 10:15:47 AM Β· Difficulty 11.0216 Β· 3,756,259 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a8272253d459fafe5464e97da5f7a4883a3fde4faf6db362dbe8a55815918639
View on Chainz β†—

Difficulty

11.021578

Transactions

2

Size

1.14 KB

Version

2

Bits

0b058625

Nonce

269,641,239

Timestamp

3/7/2019, 10:15:47 AM

Confirmations

3,756,259

Merkle Root

f193a9cd02120858c7606c12ce83c0982e403950cf2be3a19384d43fb9a3b900
Transactions (2)
Coinbasefc52acb337f983…255affd3ebd23d
1 in β†’ 1 out8.2400 XPM110 B
AUhjokok…k5m93PZR
9eff9b35a0f974…79595638a10971
6 in β†’ 2 out1069.3171 XPM967 B
AZQgL5kt…6NE43uZsAHgwGWSe…DFXcbtYB
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.

5.984 Γ— 10⁹⁴(95-digit number)
59849301268817978973…10203567239429598800
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
5.984 Γ— 10⁹⁴(95-digit number)
59849301268817978973…10203567239429598799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.984 Γ— 10⁹⁴(95-digit number)
59849301268817978973…10203567239429598801
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
1.196 Γ— 10⁹⁡(96-digit number)
11969860253763595794…20407134478859197599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.196 Γ— 10⁹⁡(96-digit number)
11969860253763595794…20407134478859197601
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
2.393 Γ— 10⁹⁡(96-digit number)
23939720507527191589…40814268957718395199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.393 Γ— 10⁹⁡(96-digit number)
23939720507527191589…40814268957718395201
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
4.787 Γ— 10⁹⁡(96-digit number)
47879441015054383178…81628537915436790399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.787 Γ— 10⁹⁡(96-digit number)
47879441015054383178…81628537915436790401
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
9.575 Γ— 10⁹⁡(96-digit number)
95758882030108766357…63257075830873580799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.575 Γ— 10⁹⁡(96-digit number)
95758882030108766357…63257075830873580801
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
1.915 Γ— 10⁹⁢(97-digit number)
19151776406021753271…26514151661747161599
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 3082328

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 a8272253d459fafe5464e97da5f7a4883a3fde4faf6db362dbe8a55815918639

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 #3,082,328 on Chainz β†—
Circulating Supply:57,952,982 XPMΒ·at block #6,838,586 Β· updates every 60s
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