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Home/Chain Registry/Block #2,287,326

Block #2,287,326

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/8/2017, 4:23:42 AM Β· Difficulty 10.9555 Β· 4,545,029 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e62589e6f17d5dffdc8529b4ced5989c388e277dfcea41eb792478fa7fdb5579
View on Chainz β†—

Difficulty

10.955550

Transactions

1

Size

198 B

Version

2

Bits

0af49eec

Nonce

986,775,471

Timestamp

9/8/2017, 4:23:42 AM

Confirmations

4,545,029

Merkle Root

182d3954c4b93a82a32e7a1322c75255c388bfd139f5d643db7aa5a73acf2119
Transactions (1)
Coinbase182d3954c4b93a…7aa5a73acf2119
1 in β†’ 1 out8.3200 XPM109 B
AXEgv48K…A2fjM2oY
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.

1.869 Γ— 10⁹³(94-digit number)
18699646523483477408…53705200924267656000
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
1.869 Γ— 10⁹³(94-digit number)
18699646523483477408…53705200924267655999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.869 Γ— 10⁹³(94-digit number)
18699646523483477408…53705200924267656001
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
3.739 Γ— 10⁹³(94-digit number)
37399293046966954817…07410401848535311999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.739 Γ— 10⁹³(94-digit number)
37399293046966954817…07410401848535312001
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
7.479 Γ— 10⁹³(94-digit number)
74798586093933909634…14820803697070623999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.479 Γ— 10⁹³(94-digit number)
74798586093933909634…14820803697070624001
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
1.495 Γ— 10⁹⁴(95-digit number)
14959717218786781926…29641607394141247999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.495 Γ— 10⁹⁴(95-digit number)
14959717218786781926…29641607394141248001
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
2.991 Γ— 10⁹⁴(95-digit number)
29919434437573563853…59283214788282495999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.991 Γ— 10⁹⁴(95-digit number)
29919434437573563853…59283214788282496001
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 2287326

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 e62589e6f17d5dffdc8529b4ced5989c388e277dfcea41eb792478fa7fdb5579

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 #2,287,326 on Chainz β†—
Circulating Supply:57,902,988 XPMΒ·at block #6,832,354 Β· updates every 60s
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