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Home/Chain Registry/Block #3,223,884

Block #3,223,884

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/13/2019, 6:44:04 PM Β· Difficulty 11.0151 Β· 3,618,281 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
416e93451010ed2d1d4a850b18404662db2383d3fada18c0230bf8accf512667
View on Chainz β†—

Difficulty

11.015087

Transactions

1

Size

201 B

Version

2

Bits

0b03dcc0

Nonce

886,345,786

Timestamp

6/13/2019, 6:44:04 PM

Confirmations

3,618,281

Merkle Root

f261c48d95c3a29c88e7ffa680633f1629ba24daf36ffacfb32c0d87ae0ddaf2
Transactions (1)
Coinbasef261c48d95c3a2…2c0d87ae0ddaf2
1 in β†’ 1 out8.2300 XPM110 B
AbXwmGxD…4XXYP765
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.

5.112 Γ— 10⁹⁷(98-digit number)
51121342702683922031…80819479787075338240
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
5.112 Γ— 10⁹⁷(98-digit number)
51121342702683922031…80819479787075338239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.112 Γ— 10⁹⁷(98-digit number)
51121342702683922031…80819479787075338241
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
1.022 Γ— 10⁹⁸(99-digit number)
10224268540536784406…61638959574150676479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.022 Γ— 10⁹⁸(99-digit number)
10224268540536784406…61638959574150676481
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
2.044 Γ— 10⁹⁸(99-digit number)
20448537081073568812…23277919148301352959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.044 Γ— 10⁹⁸(99-digit number)
20448537081073568812…23277919148301352961
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
4.089 Γ— 10⁹⁸(99-digit number)
40897074162147137625…46555838296602705919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.089 Γ— 10⁹⁸(99-digit number)
40897074162147137625…46555838296602705921
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
8.179 Γ— 10⁹⁸(99-digit number)
81794148324294275251…93111676593205411839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.179 Γ— 10⁹⁸(99-digit number)
81794148324294275251…93111676593205411841
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
1.635 Γ— 10⁹⁹(100-digit number)
16358829664858855050…86223353186410823679
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 3223884

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 416e93451010ed2d1d4a850b18404662db2383d3fada18c0230bf8accf512667

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 #3,223,884 on Chainz β†—
Circulating Supply:57,981,711 XPMΒ·at block #6,842,164 Β· updates every 60s
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