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Block #326,558

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/23/2013, 9:35:35 PM Β· Difficulty 10.1880 Β· 6,490,708 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2b631b4db36d09730a7938e78bb38f8262e38fb12ceb7929fdb8a63b17647206
View on Chainz β†—

Height

#326,558

Difficulty

10.187961

Transactions

1

Size

210 B

Version

2

Bits

0a301e3e

Nonce

43,136

Timestamp

12/23/2013, 9:35:35 PM

Confirmations

6,490,708

Merkle Root

24d62a844805f24fcd1caff2f859f79d69a418fcfa87cf7cda434b1f297901b9
Transactions (1)
Coinbase24d62a844805f2…434b1f297901b9
1 in β†’ 1 out9.6200 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.

8.188 Γ— 10¹⁰⁴(105-digit number)
81882741582711567681…79206518883594528160
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
8.188 Γ— 10¹⁰⁴(105-digit number)
81882741582711567681…79206518883594528159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.188 Γ— 10¹⁰⁴(105-digit number)
81882741582711567681…79206518883594528161
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
1.637 Γ— 10¹⁰⁡(106-digit number)
16376548316542313536…58413037767189056319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.637 Γ— 10¹⁰⁡(106-digit number)
16376548316542313536…58413037767189056321
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
3.275 Γ— 10¹⁰⁡(106-digit number)
32753096633084627072…16826075534378112639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.275 Γ— 10¹⁰⁡(106-digit number)
32753096633084627072…16826075534378112641
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
6.550 Γ— 10¹⁰⁡(106-digit number)
65506193266169254145…33652151068756225279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.550 Γ— 10¹⁰⁡(106-digit number)
65506193266169254145…33652151068756225281
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
1.310 Γ— 10¹⁰⁢(107-digit number)
13101238653233850829…67304302137512450559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.310 Γ— 10¹⁰⁢(107-digit number)
13101238653233850829…67304302137512450561
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 326558

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 2b631b4db36d09730a7938e78bb38f8262e38fb12ceb7929fdb8a63b17647206

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 #326,558 on Chainz β†—
Circulating Supply:57,782,165 XPMΒ·at block #6,817,265 Β· updates every 60s
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