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Home/Chain Registry/Block #2,643,991

Block #2,643,991

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/2/2018, 7:39:01 AM Β· Difficulty 11.6992 Β· 4,196,450 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2a04abe1ca5d6dba2b96e6550a7622ac155ce74c8b8875d47d3627895a500c88
View on Chainz β†—

Difficulty

11.699158

Transactions

1

Size

200 B

Version

2

Bits

0bb2fc07

Nonce

419,904,248

Timestamp

5/2/2018, 7:39:01 AM

Confirmations

4,196,450

Merkle Root

05cc1852f382e97cb3f35ad307134e9f109b93cca0bb9770a2133ddff4d636e4
Transactions (1)
Coinbase05cc1852f382e9…133ddff4d636e4
1 in β†’ 1 out7.2900 XPM110 B
APCEzroB…AuW8XrGU
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.

1.273 Γ— 10⁹⁡(96-digit number)
12731403265977903281…12152422772334448640
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
1.273 Γ— 10⁹⁡(96-digit number)
12731403265977903281…12152422772334448639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.273 Γ— 10⁹⁡(96-digit number)
12731403265977903281…12152422772334448641
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
2.546 Γ— 10⁹⁡(96-digit number)
25462806531955806562…24304845544668897279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.546 Γ— 10⁹⁡(96-digit number)
25462806531955806562…24304845544668897281
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
5.092 Γ— 10⁹⁡(96-digit number)
50925613063911613125…48609691089337794559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.092 Γ— 10⁹⁡(96-digit number)
50925613063911613125…48609691089337794561
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
1.018 Γ— 10⁹⁢(97-digit number)
10185122612782322625…97219382178675589119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.018 Γ— 10⁹⁢(97-digit number)
10185122612782322625…97219382178675589121
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
2.037 Γ— 10⁹⁢(97-digit number)
20370245225564645250…94438764357351178239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.037 Γ— 10⁹⁢(97-digit number)
20370245225564645250…94438764357351178241
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
4.074 Γ— 10⁹⁢(97-digit number)
40740490451129290500…88877528714702356479
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 2643991

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 2a04abe1ca5d6dba2b96e6550a7622ac155ce74c8b8875d47d3627895a500c88

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 #2,643,991 on Chainz β†—
Circulating Supply:57,967,857 XPMΒ·at block #6,840,440 Β· updates every 60s
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