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Home/Chain Registry/Block #2,723,007

Block #2,723,007

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/27/2018, 1:45:26 AM Β· Difficulty 11.6162 Β· 4,122,221 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6811e7bb4e994c85f6ddd6148e22fc9ac4aaba8ddc3be4da3fade50fb95ba5d6
View on Chainz β†—

Difficulty

11.616198

Transactions

1

Size

200 B

Version

2

Bits

0b9dbf21

Nonce

141,180,579

Timestamp

6/27/2018, 1:45:26 AM

Confirmations

4,122,221

Merkle Root

51d18aa36c7e1b9540649515d42627867f0715a179624093d28fdb021144c8db
Transactions (1)
Coinbase51d18aa36c7e1b…8fdb021144c8db
1 in β†’ 1 out7.4000 XPM110 B
AZtxQr2F…7grUWrUz
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.

2.684 Γ— 10⁹⁴(95-digit number)
26840276319748164517…24751689487919162040
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
2.684 Γ— 10⁹⁴(95-digit number)
26840276319748164517…24751689487919162039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.684 Γ— 10⁹⁴(95-digit number)
26840276319748164517…24751689487919162041
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
5.368 Γ— 10⁹⁴(95-digit number)
53680552639496329035…49503378975838324079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.368 Γ— 10⁹⁴(95-digit number)
53680552639496329035…49503378975838324081
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
1.073 Γ— 10⁹⁡(96-digit number)
10736110527899265807…99006757951676648159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.073 Γ— 10⁹⁡(96-digit number)
10736110527899265807…99006757951676648161
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
2.147 Γ— 10⁹⁡(96-digit number)
21472221055798531614…98013515903353296319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.147 Γ— 10⁹⁡(96-digit number)
21472221055798531614…98013515903353296321
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
4.294 Γ— 10⁹⁡(96-digit number)
42944442111597063228…96027031806706592639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.294 Γ— 10⁹⁡(96-digit number)
42944442111597063228…96027031806706592641
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
8.588 Γ— 10⁹⁡(96-digit number)
85888884223194126456…92054063613413185279
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 2723007

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 6811e7bb4e994c85f6ddd6148e22fc9ac4aaba8ddc3be4da3fade50fb95ba5d6

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 #2,723,007 on Chainz β†—
Circulating Supply:58,006,256 XPMΒ·at block #6,845,227 Β· updates every 60s
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