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Home/Chain Registry/Block #2,668,306

Block #2,668,306

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/19/2018, 11:19:54 AM Β· Difficulty 11.6762 Β· 4,170,895 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3184dc10dae001ebf14c1a9701c72a1ec9f2e7bffdcb9919bd6efbe840b17564
View on Chainz β†—

Difficulty

11.676190

Transactions

1

Size

200 B

Version

2

Bits

0bad1ac4

Nonce

21,569,033

Timestamp

5/19/2018, 11:19:54 AM

Confirmations

4,170,895

Merkle Root

c70d0be3249c9dda51c537cdd12d9d652e874d3f93378f4773c32e4eba489b28
Transactions (1)
Coinbasec70d0be3249c9d…c32e4eba489b28
1 in β†’ 1 out7.3200 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.

6.852 Γ— 10⁹⁴(95-digit number)
68528759219833661928…35528495450648454400
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
6.852 Γ— 10⁹⁴(95-digit number)
68528759219833661928…35528495450648454399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.852 Γ— 10⁹⁴(95-digit number)
68528759219833661928…35528495450648454401
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
1.370 Γ— 10⁹⁡(96-digit number)
13705751843966732385…71056990901296908799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.370 Γ— 10⁹⁡(96-digit number)
13705751843966732385…71056990901296908801
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
2.741 Γ— 10⁹⁡(96-digit number)
27411503687933464771…42113981802593817599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.741 Γ— 10⁹⁡(96-digit number)
27411503687933464771…42113981802593817601
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
5.482 Γ— 10⁹⁡(96-digit number)
54823007375866929542…84227963605187635199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.482 Γ— 10⁹⁡(96-digit number)
54823007375866929542…84227963605187635201
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
1.096 Γ— 10⁹⁢(97-digit number)
10964601475173385908…68455927210375270399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.096 Γ— 10⁹⁢(97-digit number)
10964601475173385908…68455927210375270401
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
2.192 Γ— 10⁹⁢(97-digit number)
21929202950346771817…36911854420750540799
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 2668306

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 3184dc10dae001ebf14c1a9701c72a1ec9f2e7bffdcb9919bd6efbe840b17564

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 #2,668,306 on Chainz β†—
Circulating Supply:57,957,887 XPMΒ·at block #6,839,200 Β· updates every 60s
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