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Home/Chain Registry/Block #2,651,028

Block #2,651,028

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/6/2018, 12:36:29 PM Β· Difficulty 11.7526 Β· 4,191,507 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
13d347f243d1e6c91c3ab4bd9ee722282f371fcaf32a95e9bc6396b38b0d035a
View on Chainz β†—

Difficulty

11.752577

Transactions

1

Size

201 B

Version

2

Bits

0bc0a8e6

Nonce

215,323,188

Timestamp

5/6/2018, 12:36:29 PM

Confirmations

4,191,507

Merkle Root

d556b3dbbd5628ef63aab6fe4d981a6862736b2179980933a15f8a819c88d927
Transactions (1)
Coinbased556b3dbbd5628…5f8a819c88d927
1 in β†’ 1 out7.2300 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.

1.822 Γ— 10⁹⁢(97-digit number)
18228335424760502857…04710290501831490560
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
1.822 Γ— 10⁹⁢(97-digit number)
18228335424760502857…04710290501831490559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.822 Γ— 10⁹⁢(97-digit number)
18228335424760502857…04710290501831490561
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
3.645 Γ— 10⁹⁢(97-digit number)
36456670849521005714…09420581003662981119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.645 Γ— 10⁹⁢(97-digit number)
36456670849521005714…09420581003662981121
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
7.291 Γ— 10⁹⁢(97-digit number)
72913341699042011429…18841162007325962239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.291 Γ— 10⁹⁢(97-digit number)
72913341699042011429…18841162007325962241
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
1.458 Γ— 10⁹⁷(98-digit number)
14582668339808402285…37682324014651924479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.458 Γ— 10⁹⁷(98-digit number)
14582668339808402285…37682324014651924481
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
2.916 Γ— 10⁹⁷(98-digit number)
29165336679616804571…75364648029303848959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.916 Γ— 10⁹⁷(98-digit number)
29165336679616804571…75364648029303848961
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
5.833 Γ— 10⁹⁷(98-digit number)
58330673359233609143…50729296058607697919
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 2651028

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 13d347f243d1e6c91c3ab4bd9ee722282f371fcaf32a95e9bc6396b38b0d035a

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 #2,651,028 on Chainz β†—
Circulating Supply:57,984,702 XPMΒ·at block #6,842,534 Β· updates every 60s
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