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Home/Chain Registry/Block #2,009,005

Block #2,009,005

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/5/2017, 4:08:17 AM Β· Difficulty 10.7018 Β· 4,832,450 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e1915a8d64e0c9dece17e001439230ecbbb636decec7d62b2b18b40c891128e6
View on Chainz β†—

Difficulty

10.701813

Transactions

1

Size

199 B

Version

2

Bits

0ab3aa06

Nonce

387,312,626

Timestamp

3/5/2017, 4:08:17 AM

Confirmations

4,832,450

Merkle Root

6131fb19626c92e68d7f067c10028b71eccc149b98750b2ca08070f41b6883fc
Transactions (1)
Coinbase6131fb19626c92…8070f41b6883fc
1 in β†’ 1 out8.7200 XPM109 B
AQ1LeMWt…AnDEQQH1
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.

2.179 Γ— 10⁹⁴(95-digit number)
21791588477832458763…24257351686942505040
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
2.179 Γ— 10⁹⁴(95-digit number)
21791588477832458763…24257351686942505039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.179 Γ— 10⁹⁴(95-digit number)
21791588477832458763…24257351686942505041
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
4.358 Γ— 10⁹⁴(95-digit number)
43583176955664917526…48514703373885010079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.358 Γ— 10⁹⁴(95-digit number)
43583176955664917526…48514703373885010081
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
8.716 Γ— 10⁹⁴(95-digit number)
87166353911329835052…97029406747770020159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.716 Γ— 10⁹⁴(95-digit number)
87166353911329835052…97029406747770020161
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
1.743 Γ— 10⁹⁡(96-digit number)
17433270782265967010…94058813495540040319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.743 Γ— 10⁹⁡(96-digit number)
17433270782265967010…94058813495540040321
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
3.486 Γ— 10⁹⁡(96-digit number)
34866541564531934020…88117626991080080639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.486 Γ— 10⁹⁡(96-digit number)
34866541564531934020…88117626991080080641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2009005

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 e1915a8d64e0c9dece17e001439230ecbbb636decec7d62b2b18b40c891128e6

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 #2,009,005 on Chainz β†—
Circulating Supply:57,976,020 XPMΒ·at block #6,841,454 Β· updates every 60s
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