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Block #605,730

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/28/2014, 5:14:09 PM Β· Difficulty 10.9101 Β· 6,221,525 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
995676f26da05cfd50f5aa4617594b9c6bc4d0e9dbb5e4b44a8a7b9362b111cd
View on Chainz β†—

Height

#605,730

Difficulty

10.910112

Transactions

1

Size

209 B

Version

2

Bits

0ae8fd18

Nonce

75,411,828

Timestamp

6/28/2014, 5:14:09 PM

Confirmations

6,221,525

Merkle Root

2edcc6b53d703574b320e679a7dcfcf126e666e9f7cabfcd3187a86601463fcf
Transactions (1)
Coinbase2edcc6b53d7035…87a86601463fcf
1 in β†’ 1 out8.3900 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.

4.341 Γ— 10¹⁰¹(102-digit number)
43411417553492392241…40468968551508869120
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
4.341 Γ— 10¹⁰¹(102-digit number)
43411417553492392241…40468968551508869119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.341 Γ— 10¹⁰¹(102-digit number)
43411417553492392241…40468968551508869121
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
8.682 Γ— 10¹⁰¹(102-digit number)
86822835106984784482…80937937103017738239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.682 Γ— 10¹⁰¹(102-digit number)
86822835106984784482…80937937103017738241
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
1.736 Γ— 10¹⁰²(103-digit number)
17364567021396956896…61875874206035476479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.736 Γ— 10¹⁰²(103-digit number)
17364567021396956896…61875874206035476481
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
3.472 Γ— 10¹⁰²(103-digit number)
34729134042793913792…23751748412070952959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.472 Γ— 10¹⁰²(103-digit number)
34729134042793913792…23751748412070952961
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
6.945 Γ— 10¹⁰²(103-digit number)
69458268085587827585…47503496824141905919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.945 Γ— 10¹⁰²(103-digit number)
69458268085587827585…47503496824141905921
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 605730

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 995676f26da05cfd50f5aa4617594b9c6bc4d0e9dbb5e4b44a8a7b9362b111cd

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 #605,730 on Chainz β†—
Circulating Supply:57,862,144 XPMΒ·at block #6,827,254 Β· updates every 60s
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