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Home/Chain Registry/Block #2,577,184

Block #2,577,184

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/21/2018, 5:38:41 AM Β· Difficulty 10.9959 Β· 4,268,466 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
315b0ec4918468c95c5032b919e8369af4f402ffcb850f0e02a6192f059c7418
View on Chainz β†—

Difficulty

10.995894

Transactions

1

Size

200 B

Version

2

Bits

0afef2ef

Nonce

150,547,233

Timestamp

3/21/2018, 5:38:41 AM

Confirmations

4,268,466

Merkle Root

64800e892d624196a3f195c6c4ce300d753d29a86fcbb10f8b791576720fa2d8
Transactions (1)
Coinbase64800e892d6241…791576720fa2d8
1 in β†’ 1 out8.2600 XPM110 B
Adqah8zh…1WwoHJ9t
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.

4.084 Γ— 10⁹³(94-digit number)
40847286384681712859…35317306040261989160
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
4.084 Γ— 10⁹³(94-digit number)
40847286384681712859…35317306040261989159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.084 Γ— 10⁹³(94-digit number)
40847286384681712859…35317306040261989161
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
8.169 Γ— 10⁹³(94-digit number)
81694572769363425719…70634612080523978319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.169 Γ— 10⁹³(94-digit number)
81694572769363425719…70634612080523978321
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
1.633 Γ— 10⁹⁴(95-digit number)
16338914553872685143…41269224161047956639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.633 Γ— 10⁹⁴(95-digit number)
16338914553872685143…41269224161047956641
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
3.267 Γ— 10⁹⁴(95-digit number)
32677829107745370287…82538448322095913279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.267 Γ— 10⁹⁴(95-digit number)
32677829107745370287…82538448322095913281
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
6.535 Γ— 10⁹⁴(95-digit number)
65355658215490740575…65076896644191826559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.535 Γ— 10⁹⁴(95-digit number)
65355658215490740575…65076896644191826561
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
1.307 Γ— 10⁹⁡(96-digit number)
13071131643098148115…30153793288383653119
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 2577184

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 315b0ec4918468c95c5032b919e8369af4f402ffcb850f0e02a6192f059c7418

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 #2,577,184 on Chainz β†—
Circulating Supply:58,009,649 XPMΒ·at block #6,845,649 Β· updates every 60s
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