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Block #230,811

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/28/2013, 1:21:24 AM Β· Difficulty 9.9399 Β· 6,581,413 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9a9a1e894f8ffdc921dd11edc032dbbb054fbf6120c77450b200aab57767a052
View on Chainz β†—

Height

#230,811

Difficulty

9.939907

Transactions

2

Size

355 B

Version

2

Bits

09f09dba

Nonce

35,456

Timestamp

10/28/2013, 1:21:24 AM

Confirmations

6,581,413

Merkle Root

ff20196a061f17e40a663d5bc4299e6abaa3507aa14de62f7b4d2660375e9d37
Transactions (2)
Coinbasef3870529f397e4…4a9e16e4eee4fa
1 in β†’ 1 out10.1200 XPM109 B
Achacs7V…mr8o9zxn
d96cbbb3ea0eee…51a5d4af280fbf
1 in β†’ 1 out10.1500 XPM157 B
ANPZmotn…Vo7H4mPW
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.

7.083 Γ— 10⁹¹(92-digit number)
70837268598873435029…12009189601352650080
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
7.083 Γ— 10⁹¹(92-digit number)
70837268598873435029…12009189601352650079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.083 Γ— 10⁹¹(92-digit number)
70837268598873435029…12009189601352650081
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
1.416 Γ— 10⁹²(93-digit number)
14167453719774687005…24018379202705300159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.416 Γ— 10⁹²(93-digit number)
14167453719774687005…24018379202705300161
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
2.833 Γ— 10⁹²(93-digit number)
28334907439549374011…48036758405410600319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.833 Γ— 10⁹²(93-digit number)
28334907439549374011…48036758405410600321
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
5.666 Γ— 10⁹²(93-digit number)
56669814879098748023…96073516810821200639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.666 Γ— 10⁹²(93-digit number)
56669814879098748023…96073516810821200641
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
1.133 Γ— 10⁹³(94-digit number)
11333962975819749604…92147033621642401279
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 230811

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 9a9a1e894f8ffdc921dd11edc032dbbb054fbf6120c77450b200aab57767a052

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 #230,811 on Chainz β†—
Circulating Supply:57,741,807 XPMΒ·at block #6,812,223 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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