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Block #445,201

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/15/2014, 5:46:29 PM Β· Difficulty 10.3563 Β· 6,366,513 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b5b8c577dfd856fb009df73b78af10675ec753429fccfdb3c3038b4ab70cc27a
View on Chainz β†—

Height

#445,201

Difficulty

10.356289

Transactions

2

Size

16.32 KB

Version

2

Bits

0a5b35c7

Nonce

240,730

Timestamp

3/15/2014, 5:46:29 PM

Confirmations

6,366,513

Merkle Root

b23d7ad200f220a896d74a89e7231663c6da3136cc213ccc1f99e7273310fd1f
Transactions (2)
Coinbasef80b7665a601a0…73b0733040000e
1 in β†’ 1 out9.4800 XPM110 B
AeKNrjNj…1NEq95Ta
1579e5c8b0f669…2bb5f2770884be
111 in β†’ 2 out309.7290 XPM16.12 KB
AS6wjyQC…E2BfJdMNAT23jZgt…84fQfnuy
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.

1.140 Γ— 10⁹⁷(98-digit number)
11408846334111056240…39484752196978038840
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
1.140 Γ— 10⁹⁷(98-digit number)
11408846334111056240…39484752196978038839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.140 Γ— 10⁹⁷(98-digit number)
11408846334111056240…39484752196978038841
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
2.281 Γ— 10⁹⁷(98-digit number)
22817692668222112480…78969504393956077679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.281 Γ— 10⁹⁷(98-digit number)
22817692668222112480…78969504393956077681
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
4.563 Γ— 10⁹⁷(98-digit number)
45635385336444224961…57939008787912155359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.563 Γ— 10⁹⁷(98-digit number)
45635385336444224961…57939008787912155361
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
9.127 Γ— 10⁹⁷(98-digit number)
91270770672888449923…15878017575824310719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.127 Γ— 10⁹⁷(98-digit number)
91270770672888449923…15878017575824310721
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
1.825 Γ— 10⁹⁸(99-digit number)
18254154134577689984…31756035151648621439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.825 Γ— 10⁹⁸(99-digit number)
18254154134577689984…31756035151648621441
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 445201

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 b5b8c577dfd856fb009df73b78af10675ec753429fccfdb3c3038b4ab70cc27a

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 #445,201 on Chainz β†—
Circulating Supply:57,737,824 XPMΒ·at block #6,811,713 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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