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Home/Chain Registry/Block #2,647,379

Block #2,647,379

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/3/2018, 9:42:36 PM Β· Difficulty 11.7585 Β· 4,189,788 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ab50b260c9536b1affad697d482fef9c78e70f515c6456b48588c6e825e3a24c
View on Chainz β†—

Difficulty

11.758520

Transactions

2

Size

721 B

Version

2

Bits

0bc22e56

Nonce

71,887,583

Timestamp

5/3/2018, 9:42:36 PM

Confirmations

4,189,788

Merkle Root

4c840677580bf10036ae0383b8ad0645b745fb1fc4988f8527c1af625788cafe
Transactions (2)
Coinbase9dabbb906409fa…8955e3b93acebb
1 in β†’ 1 out7.2300 XPM110 B
AWqw1EGa…p8L2DkXG
905511ed47caba…b59c58aabf6de4
3 in β†’ 2 out68.0715 XPM521 B
AaYkieLK…1eLs6Q17ASo3gm2c…giXSsoY1
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.

1.013 Γ— 10⁹⁡(96-digit number)
10132699108153905479…52260140825714394750
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
1.013 Γ— 10⁹⁡(96-digit number)
10132699108153905479…52260140825714394749
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.013 Γ— 10⁹⁡(96-digit number)
10132699108153905479…52260140825714394751
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
2.026 Γ— 10⁹⁡(96-digit number)
20265398216307810958…04520281651428789499
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.026 Γ— 10⁹⁡(96-digit number)
20265398216307810958…04520281651428789501
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
4.053 Γ— 10⁹⁡(96-digit number)
40530796432615621917…09040563302857578999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.053 Γ— 10⁹⁡(96-digit number)
40530796432615621917…09040563302857579001
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
8.106 Γ— 10⁹⁡(96-digit number)
81061592865231243834…18081126605715157999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.106 Γ— 10⁹⁡(96-digit number)
81061592865231243834…18081126605715158001
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
1.621 Γ— 10⁹⁢(97-digit number)
16212318573046248766…36162253211430315999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.621 Γ— 10⁹⁢(97-digit number)
16212318573046248766…36162253211430316001
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
3.242 Γ— 10⁹⁢(97-digit number)
32424637146092497533…72324506422860631999
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 2647379

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 ab50b260c9536b1affad697d482fef9c78e70f515c6456b48588c6e825e3a24c

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 #2,647,379 on Chainz β†—
Circulating Supply:57,941,649 XPMΒ·at block #6,837,166 Β· updates every 60s
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