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Block #645,892

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/24/2014, 10:45:33 AM Β· Difficulty 10.9528 Β· 6,181,107 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9a58b3a47ebb30db7482d920aabada4ded3128267228dc87648a7a2b4d20f565
View on Chainz β†—

Height

#645,892

Difficulty

10.952834

Transactions

1

Size

207 B

Version

2

Bits

0af3eceb

Nonce

6,496

Timestamp

7/24/2014, 10:45:33 AM

Confirmations

6,181,107

Merkle Root

9387384a99ac098c4a8d95a54b4cf428154b334ac26e1587f56db8a251450025
Transactions (1)
Coinbase9387384a99ac09…6db8a251450025
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
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.

6.141 Γ— 10⁹⁷(98-digit number)
61419186529490735423…57675455374698704320
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
6.141 Γ— 10⁹⁷(98-digit number)
61419186529490735423…57675455374698704319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.141 Γ— 10⁹⁷(98-digit number)
61419186529490735423…57675455374698704321
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
1.228 Γ— 10⁹⁸(99-digit number)
12283837305898147084…15350910749397408639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.228 Γ— 10⁹⁸(99-digit number)
12283837305898147084…15350910749397408641
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
2.456 Γ— 10⁹⁸(99-digit number)
24567674611796294169…30701821498794817279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.456 Γ— 10⁹⁸(99-digit number)
24567674611796294169…30701821498794817281
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
4.913 Γ— 10⁹⁸(99-digit number)
49135349223592588339…61403642997589634559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.913 Γ— 10⁹⁸(99-digit number)
49135349223592588339…61403642997589634561
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
9.827 Γ— 10⁹⁸(99-digit number)
98270698447185176678…22807285995179269119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.827 Γ— 10⁹⁸(99-digit number)
98270698447185176678…22807285995179269121
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 645892

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 9a58b3a47ebb30db7482d920aabada4ded3128267228dc87648a7a2b4d20f565

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 #645,892 on Chainz β†—
Circulating Supply:57,860,168 XPMΒ·at block #6,826,998 Β· updates every 60s
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