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Block #440,464

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/12/2014, 10:51:37 AM Β· Difficulty 10.3529 Β· 6,354,518 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1ccca6721d612ecc03f1f976f4795f3ffd1a9187855110bfa5e50d9a4b08e760
View on Chainz β†—

Height

#440,464

Difficulty

10.352940

Transactions

1

Size

208 B

Version

2

Bits

0a5a5a40

Nonce

446,928

Timestamp

3/12/2014, 10:51:37 AM

Confirmations

6,354,518

Merkle Root

d021870ca6037443cd7abde86dc1c2545aef9e9701d7053081cfbdfcf0741b18
Transactions (1)
Coinbased021870ca60374…cfbdfcf0741b18
1 in β†’ 1 out9.3200 XPM116 B
AbwWkWZt…kawDhufa
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.

1.757 Γ— 10⁹⁹(100-digit number)
17579058630829011648…75372092928260016000
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
1.757 Γ— 10⁹⁹(100-digit number)
17579058630829011648…75372092928260015999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.757 Γ— 10⁹⁹(100-digit number)
17579058630829011648…75372092928260016001
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
3.515 Γ— 10⁹⁹(100-digit number)
35158117261658023296…50744185856520031999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.515 Γ— 10⁹⁹(100-digit number)
35158117261658023296…50744185856520032001
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
7.031 Γ— 10⁹⁹(100-digit number)
70316234523316046593…01488371713040063999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.031 Γ— 10⁹⁹(100-digit number)
70316234523316046593…01488371713040064001
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
1.406 Γ— 10¹⁰⁰(101-digit number)
14063246904663209318…02976743426080127999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.406 Γ— 10¹⁰⁰(101-digit number)
14063246904663209318…02976743426080128001
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
2.812 Γ— 10¹⁰⁰(101-digit number)
28126493809326418637…05953486852160255999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.812 Γ— 10¹⁰⁰(101-digit number)
28126493809326418637…05953486852160256001
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 440464

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 1ccca6721d612ecc03f1f976f4795f3ffd1a9187855110bfa5e50d9a4b08e760

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 #440,464 on Chainz β†—
Circulating Supply:57,603,897 XPMΒ·at block #6,794,981 Β· updates every 60s
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