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Home/Chain Registry/Block #2,723,008

Block #2,723,008

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/27/2018, 1:46:05 AM Β· Difficulty 11.6162 Β· 4,122,642 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ca6c638348c0d89d13d378798daf21a20e3d3b7e17011ae060750a8ebc0cb164
View on Chainz β†—

Difficulty

11.616250

Transactions

1

Size

200 B

Version

2

Bits

0b9dc28a

Nonce

868,812,677

Timestamp

6/27/2018, 1:46:05 AM

Confirmations

4,122,642

Merkle Root

0df00ebcf669da1138995b844b14d7ba7a0b80bba8764def5463ff561508f2c9
Transactions (1)
Coinbase0df00ebcf669da…63ff561508f2c9
1 in β†’ 1 out7.4000 XPM110 B
AbnihbJV…dbLRSVUj
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.

3.289 Γ— 10⁹³(94-digit number)
32895768801497952481…83217877925755687600
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
3.289 Γ— 10⁹³(94-digit number)
32895768801497952481…83217877925755687599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.289 Γ— 10⁹³(94-digit number)
32895768801497952481…83217877925755687601
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
6.579 Γ— 10⁹³(94-digit number)
65791537602995904963…66435755851511375199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.579 Γ— 10⁹³(94-digit number)
65791537602995904963…66435755851511375201
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
1.315 Γ— 10⁹⁴(95-digit number)
13158307520599180992…32871511703022750399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.315 Γ— 10⁹⁴(95-digit number)
13158307520599180992…32871511703022750401
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
2.631 Γ— 10⁹⁴(95-digit number)
26316615041198361985…65743023406045500799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.631 Γ— 10⁹⁴(95-digit number)
26316615041198361985…65743023406045500801
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
5.263 Γ— 10⁹⁴(95-digit number)
52633230082396723970…31486046812091001599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.263 Γ— 10⁹⁴(95-digit number)
52633230082396723970…31486046812091001601
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
1.052 Γ— 10⁹⁡(96-digit number)
10526646016479344794…62972093624182003199
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 2723008

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 ca6c638348c0d89d13d378798daf21a20e3d3b7e17011ae060750a8ebc0cb164

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 #2,723,008 on Chainz β†—
Circulating Supply:58,009,649 XPMΒ·at block #6,845,649 Β· updates every 60s
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