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Home/Chain Registry/Block #2,284,636

Block #2,284,636

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/6/2017, 8:11:15 AM Β· Difficulty 10.9551 Β· 4,557,352 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c45a39f2516dc0cca714dcf15d4dcf81636b93e8048f7707fd3b82b5cb709d40
View on Chainz β†—

Difficulty

10.955143

Transactions

1

Size

200 B

Version

2

Bits

0af48440

Nonce

1,130,860,302

Timestamp

9/6/2017, 8:11:15 AM

Confirmations

4,557,352

Merkle Root

89dab37c78106f0f7c5f19d6c50f2f9bbae9526da0b91ef8119a04a0dd4e1d63
Transactions (1)
Coinbase89dab37c78106f…9a04a0dd4e1d63
1 in β†’ 1 out8.3200 XPM110 B
AJK6MyLy…g5jN4nNB
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.

6.207 Γ— 10⁹⁴(95-digit number)
62076971136983075166…29654405424571298080
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
6.207 Γ— 10⁹⁴(95-digit number)
62076971136983075166…29654405424571298079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.207 Γ— 10⁹⁴(95-digit number)
62076971136983075166…29654405424571298081
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
1.241 Γ— 10⁹⁡(96-digit number)
12415394227396615033…59308810849142596159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.241 Γ— 10⁹⁡(96-digit number)
12415394227396615033…59308810849142596161
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
2.483 Γ— 10⁹⁡(96-digit number)
24830788454793230066…18617621698285192319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.483 Γ— 10⁹⁡(96-digit number)
24830788454793230066…18617621698285192321
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
4.966 Γ— 10⁹⁡(96-digit number)
49661576909586460132…37235243396570384639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.966 Γ— 10⁹⁡(96-digit number)
49661576909586460132…37235243396570384641
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
9.932 Γ— 10⁹⁡(96-digit number)
99323153819172920265…74470486793140769279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.932 Γ— 10⁹⁡(96-digit number)
99323153819172920265…74470486793140769281
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
1.986 Γ— 10⁹⁢(97-digit number)
19864630763834584053…48940973586281538559
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 2284636

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 c45a39f2516dc0cca714dcf15d4dcf81636b93e8048f7707fd3b82b5cb709d40

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 #2,284,636 on Chainz β†—
Circulating Supply:57,980,290 XPMΒ·at block #6,841,987 Β· updates every 60s
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