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Home/Chain Registry/Block #2,650,361

Block #2,650,361

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/5/2018, 11:55:25 PM Β· Difficulty 11.7571 Β· 4,189,263 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8692d2d012f76dffb1411dccb50989493505141f86e375e5e6b8d11e9c4f97a6
View on Chainz β†—

Difficulty

11.757138

Transactions

1

Size

200 B

Version

2

Bits

0bc1d3d2

Nonce

355,841,181

Timestamp

5/5/2018, 11:55:25 PM

Confirmations

4,189,263

Merkle Root

4d8a9b0f307a7a694e261b53e1f993782a1af0181d3b16d6e983e86cd97f2cc6
Transactions (1)
Coinbase4d8a9b0f307a7a…83e86cd97f2cc6
1 in β†’ 1 out7.2200 XPM110 B
AXzSc8EK…WFk8aWsC
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.

7.346 Γ— 10⁹⁴(95-digit number)
73467037096818085662…56767041460316931200
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
7.346 Γ— 10⁹⁴(95-digit number)
73467037096818085662…56767041460316931199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.346 Γ— 10⁹⁴(95-digit number)
73467037096818085662…56767041460316931201
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
1.469 Γ— 10⁹⁡(96-digit number)
14693407419363617132…13534082920633862399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.469 Γ— 10⁹⁡(96-digit number)
14693407419363617132…13534082920633862401
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
2.938 Γ— 10⁹⁡(96-digit number)
29386814838727234265…27068165841267724799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.938 Γ— 10⁹⁡(96-digit number)
29386814838727234265…27068165841267724801
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
5.877 Γ— 10⁹⁡(96-digit number)
58773629677454468530…54136331682535449599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.877 Γ— 10⁹⁡(96-digit number)
58773629677454468530…54136331682535449601
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
1.175 Γ— 10⁹⁢(97-digit number)
11754725935490893706…08272663365070899199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.175 Γ— 10⁹⁢(97-digit number)
11754725935490893706…08272663365070899201
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
2.350 Γ— 10⁹⁢(97-digit number)
23509451870981787412…16545326730141798399
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 2650361

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 8692d2d012f76dffb1411dccb50989493505141f86e375e5e6b8d11e9c4f97a6

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 #2,650,361 on Chainz β†—
Circulating Supply:57,961,284 XPMΒ·at block #6,839,623 Β· updates every 60s
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