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Block #327,066

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/24/2013, 7:10:43 AM Β· Difficulty 10.1772 Β· 6,498,208 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
522cffe127b5ded0f632ca652dac46e8e2d8ecd4390db27d2b5f4c38bd8d7c17
View on Chainz β†—

Height

#327,066

Difficulty

10.177209

Transactions

1

Size

199 B

Version

2

Bits

0a2d5d8d

Nonce

77,460

Timestamp

12/24/2013, 7:10:43 AM

Confirmations

6,498,208

Merkle Root

2aa31c7c47d0d9f34dd1689a42d9bc91359cb1e07b8d5b7b0ab501242f0180ba
Transactions (1)
Coinbase2aa31c7c47d0d9…b501242f0180ba
1 in β†’ 1 out9.6400 XPM109 B
AJi5fW5t…oSeNnqeA
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.

7.259 Γ— 10⁹⁴(95-digit number)
72595464558387072402…70755393250738486080
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
7.259 Γ— 10⁹⁴(95-digit number)
72595464558387072402…70755393250738486079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.259 Γ— 10⁹⁴(95-digit number)
72595464558387072402…70755393250738486081
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
1.451 Γ— 10⁹⁡(96-digit number)
14519092911677414480…41510786501476972159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.451 Γ— 10⁹⁡(96-digit number)
14519092911677414480…41510786501476972161
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
2.903 Γ— 10⁹⁡(96-digit number)
29038185823354828961…83021573002953944319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.903 Γ— 10⁹⁡(96-digit number)
29038185823354828961…83021573002953944321
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
5.807 Γ— 10⁹⁡(96-digit number)
58076371646709657922…66043146005907888639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.807 Γ— 10⁹⁡(96-digit number)
58076371646709657922…66043146005907888641
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
1.161 Γ— 10⁹⁢(97-digit number)
11615274329341931584…32086292011815777279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.161 Γ— 10⁹⁢(97-digit number)
11615274329341931584…32086292011815777281
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 327066

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 522cffe127b5ded0f632ca652dac46e8e2d8ecd4390db27d2b5f4c38bd8d7c17

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 #327,066 on Chainz β†—
Circulating Supply:57,846,289 XPMΒ·at block #6,825,273 Β· updates every 60s
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