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Home/Chain Registry/Block #3,082,364

Block #3,082,364

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/7/2019, 10:51:09 AM Β· Difficulty 11.0218 Β· 3,760,469 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
651aae5529337beed6dca9a4131cefe12d3a283be4d976516dd1a3ec19e1d019
View on Chainz β†—

Difficulty

11.021758

Transactions

1

Size

199 B

Version

2

Bits

0b0591e9

Nonce

1,990,160,615

Timestamp

3/7/2019, 10:51:09 AM

Confirmations

3,760,469

Merkle Root

8d88c17093d1714fbb9ae57ef2246ed9488fffd9d1049459072149e22b974bf0
Transactions (1)
Coinbase8d88c17093d171…2149e22b974bf0
1 in β†’ 1 out8.2200 XPM109 B
AbXwmGxD…4XXYP765
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.

4.482 Γ— 10⁹³(94-digit number)
44827029759909479032…03734952634173976640
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
4.482 Γ— 10⁹³(94-digit number)
44827029759909479032…03734952634173976639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.482 Γ— 10⁹³(94-digit number)
44827029759909479032…03734952634173976641
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
8.965 Γ— 10⁹³(94-digit number)
89654059519818958064…07469905268347953279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.965 Γ— 10⁹³(94-digit number)
89654059519818958064…07469905268347953281
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
1.793 Γ— 10⁹⁴(95-digit number)
17930811903963791612…14939810536695906559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.793 Γ— 10⁹⁴(95-digit number)
17930811903963791612…14939810536695906561
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
3.586 Γ— 10⁹⁴(95-digit number)
35861623807927583225…29879621073391813119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.586 Γ— 10⁹⁴(95-digit number)
35861623807927583225…29879621073391813121
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
7.172 Γ— 10⁹⁴(95-digit number)
71723247615855166451…59759242146783626239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.172 Γ— 10⁹⁴(95-digit number)
71723247615855166451…59759242146783626241
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
1.434 Γ— 10⁹⁡(96-digit number)
14344649523171033290…19518484293567252479
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 3082364

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 651aae5529337beed6dca9a4131cefe12d3a283be4d976516dd1a3ec19e1d019

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 #3,082,364 on Chainz β†—
Circulating Supply:57,987,008 XPMΒ·at block #6,842,832 Β· updates every 60s
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