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Home/Chain Registry/Block #2,644,848

Block #2,644,848

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/2/2018, 4:11:24 PM Β· Difficulty 11.7191 Β· 4,197,572 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6b0b2a4d1a2fb5e4c297f5806ac589a71dac7547fee7c73e5db217368d7145aa
View on Chainz β†—

Difficulty

11.719080

Transactions

1

Size

201 B

Version

2

Bits

0bb815a7

Nonce

131,182,628

Timestamp

5/2/2018, 4:11:24 PM

Confirmations

4,197,572

Merkle Root

b9711959590474de8ba50667296a954d54601dd7e297b77fdebee20aed806092
Transactions (1)
Coinbaseb9711959590474…bee20aed806092
1 in β†’ 1 out7.2700 XPM110 B
Adqah8zh…1WwoHJ9t
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.

2.702 Γ— 10⁹⁷(98-digit number)
27029823314441754113…93033769846372761600
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
2.702 Γ— 10⁹⁷(98-digit number)
27029823314441754113…93033769846372761599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.702 Γ— 10⁹⁷(98-digit number)
27029823314441754113…93033769846372761601
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
5.405 Γ— 10⁹⁷(98-digit number)
54059646628883508226…86067539692745523199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.405 Γ— 10⁹⁷(98-digit number)
54059646628883508226…86067539692745523201
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
1.081 Γ— 10⁹⁸(99-digit number)
10811929325776701645…72135079385491046399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.081 Γ— 10⁹⁸(99-digit number)
10811929325776701645…72135079385491046401
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
2.162 Γ— 10⁹⁸(99-digit number)
21623858651553403290…44270158770982092799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.162 Γ— 10⁹⁸(99-digit number)
21623858651553403290…44270158770982092801
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
4.324 Γ— 10⁹⁸(99-digit number)
43247717303106806581…88540317541964185599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.324 Γ— 10⁹⁸(99-digit number)
43247717303106806581…88540317541964185601
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
8.649 Γ— 10⁹⁸(99-digit number)
86495434606213613162…77080635083928371199
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 2644848

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 6b0b2a4d1a2fb5e4c297f5806ac589a71dac7547fee7c73e5db217368d7145aa

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 #2,644,848 on Chainz β†—
Circulating Supply:57,983,774 XPMΒ·at block #6,842,419 Β· updates every 60s
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