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Block #2,820,744

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/2/2018, 2:49:48 AM Β· Difficulty 11.7001 Β· 4,023,225 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
801cf409279b3b457a0d700ac321b4dcf3ab26ce757e2c35e496f82e978ee85d
View on Chainz β†—

Difficulty

11.700057

Transactions

1

Size

200 B

Version

2

Bits

0bb336ea

Nonce

148,979,912

Timestamp

9/2/2018, 2:49:48 AM

Confirmations

4,023,225

Merkle Root

63db141b08b713a161380a9e9ec7973ed2802bae20d72cc1acee9dc746c1354b
Transactions (1)
Coinbase63db141b08b713…ee9dc746c1354b
1 in β†’ 1 out7.2900 XPM110 B
AMrRutcS…6kzaX9VY
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.

1.469 Γ— 10⁹⁡(96-digit number)
14695121409480910863…88655554796807010560
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
1.469 Γ— 10⁹⁡(96-digit number)
14695121409480910863…88655554796807010559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.469 Γ— 10⁹⁡(96-digit number)
14695121409480910863…88655554796807010561
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
2.939 Γ— 10⁹⁡(96-digit number)
29390242818961821727…77311109593614021119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.939 Γ— 10⁹⁡(96-digit number)
29390242818961821727…77311109593614021121
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
5.878 Γ— 10⁹⁡(96-digit number)
58780485637923643454…54622219187228042239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.878 Γ— 10⁹⁡(96-digit number)
58780485637923643454…54622219187228042241
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
1.175 Γ— 10⁹⁢(97-digit number)
11756097127584728690…09244438374456084479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.175 Γ— 10⁹⁢(97-digit number)
11756097127584728690…09244438374456084481
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
2.351 Γ— 10⁹⁢(97-digit number)
23512194255169457381…18488876748912168959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.351 Γ— 10⁹⁢(97-digit number)
23512194255169457381…18488876748912168961
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
4.702 Γ— 10⁹⁢(97-digit number)
47024388510338914763…36977753497824337919
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 2820744

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 801cf409279b3b457a0d700ac321b4dcf3ab26ce757e2c35e496f82e978ee85d

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 #2,820,744 on Chainz β†—
Circulating Supply:57,996,130 XPMΒ·at block #6,843,968 Β· updates every 60s
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