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Home/Chain Registry/Block #2,822,574

Block #2,822,574

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/3/2018, 8:32:08 AM Β· Difficulty 11.7030 Β· 4,019,525 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
25cb29224be305ce7de086cd360abb203368eb20aec3152a487bde0a948fcfa5
View on Chainz β†—

Difficulty

11.703050

Transactions

1

Size

201 B

Version

2

Bits

0bb3fb15

Nonce

1,638,701,877

Timestamp

9/3/2018, 8:32:08 AM

Confirmations

4,019,525

Merkle Root

39b569452dae40d801fa5444ab002ffd68cb857680e18eab5d51c72deed79696
Transactions (1)
Coinbase39b569452dae40…51c72deed79696
1 in β†’ 1 out7.2900 XPM109 B
AKDZsL7i…aaz9dKMA
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.

3.759 Γ— 10⁹⁸(99-digit number)
37599020723385619227…45472380278321315840
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
3.759 Γ— 10⁹⁸(99-digit number)
37599020723385619227…45472380278321315839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.759 Γ— 10⁹⁸(99-digit number)
37599020723385619227…45472380278321315841
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
7.519 Γ— 10⁹⁸(99-digit number)
75198041446771238455…90944760556642631679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.519 Γ— 10⁹⁸(99-digit number)
75198041446771238455…90944760556642631681
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
1.503 Γ— 10⁹⁹(100-digit number)
15039608289354247691…81889521113285263359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.503 Γ— 10⁹⁹(100-digit number)
15039608289354247691…81889521113285263361
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
3.007 Γ— 10⁹⁹(100-digit number)
30079216578708495382…63779042226570526719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.007 Γ— 10⁹⁹(100-digit number)
30079216578708495382…63779042226570526721
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
6.015 Γ— 10⁹⁹(100-digit number)
60158433157416990764…27558084453141053439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.015 Γ— 10⁹⁹(100-digit number)
60158433157416990764…27558084453141053441
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
1.203 Γ— 10¹⁰⁰(101-digit number)
12031686631483398152…55116168906282106879
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 2822574

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 25cb29224be305ce7de086cd360abb203368eb20aec3152a487bde0a948fcfa5

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 #2,822,574 on Chainz β†—
Circulating Supply:57,981,179 XPMΒ·at block #6,842,098 Β· updates every 60s
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