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Block #2,643,891

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/2/2018, 6:43:12 AM Β· Difficulty 11.6965 Β· 4,194,397 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
cdc36e7cf5d0feebb9e7a043aef51612ff707d714339ca67c5da13b2e80548a2
View on Chainz β†—

Difficulty

11.696534

Transactions

1

Size

200 B

Version

2

Bits

0bb2500f

Nonce

73,215,769

Timestamp

5/2/2018, 6:43:12 AM

Confirmations

4,194,397

Merkle Root

7a97ee94553d39750c288d2980564140a0f134e62daa43232e9fd49d3e1cd455
Transactions (1)
Coinbase7a97ee94553d39…9fd49d3e1cd455
1 in β†’ 1 out7.3000 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.

4.338 Γ— 10⁹⁴(95-digit number)
43384716184264746524…48419234257434128320
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
4.338 Γ— 10⁹⁴(95-digit number)
43384716184264746524…48419234257434128319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.338 Γ— 10⁹⁴(95-digit number)
43384716184264746524…48419234257434128321
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
8.676 Γ— 10⁹⁴(95-digit number)
86769432368529493049…96838468514868256639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.676 Γ— 10⁹⁴(95-digit number)
86769432368529493049…96838468514868256641
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
1.735 Γ— 10⁹⁡(96-digit number)
17353886473705898609…93676937029736513279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.735 Γ— 10⁹⁡(96-digit number)
17353886473705898609…93676937029736513281
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
3.470 Γ— 10⁹⁡(96-digit number)
34707772947411797219…87353874059473026559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.470 Γ— 10⁹⁡(96-digit number)
34707772947411797219…87353874059473026561
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
6.941 Γ— 10⁹⁡(96-digit number)
69415545894823594439…74707748118946053119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.941 Γ— 10⁹⁡(96-digit number)
69415545894823594439…74707748118946053121
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
1.388 Γ— 10⁹⁢(97-digit number)
13883109178964718887…49415496237892106239
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 2643891

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 cdc36e7cf5d0feebb9e7a043aef51612ff707d714339ca67c5da13b2e80548a2

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 #2,643,891 on Chainz β†—
Circulating Supply:57,950,585 XPMΒ·at block #6,838,287 Β· updates every 60s
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