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Block #242,533

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/3/2013, 7:14:32 PM Β· Difficulty 9.9601 Β· 6,588,915 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
07751d62c779a53b2d578245ebccff2b54e192d35326b2a67c4cdb2b405d63d4
View on Chainz β†—

Height

#242,533

Difficulty

9.960055

Transactions

1

Size

199 B

Version

2

Bits

09f5c630

Nonce

64,467

Timestamp

11/3/2013, 7:14:32 PM

Confirmations

6,588,915

Merkle Root

5b0a8a0c7bfcdd8bca1da26265aac5ead1127e67ab318e532059f62d791ed34c
Transactions (1)
Coinbase5b0a8a0c7bfcdd…59f62d791ed34c
1 in β†’ 1 out10.0700 XPM109 B
AQ1oEfNd…b5SXgggm
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.

1.443 Γ— 10⁹⁡(96-digit number)
14439604732592189971…94903261968750548200
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
1.443 Γ— 10⁹⁡(96-digit number)
14439604732592189971…94903261968750548199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.443 Γ— 10⁹⁡(96-digit number)
14439604732592189971…94903261968750548201
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
2.887 Γ— 10⁹⁡(96-digit number)
28879209465184379942…89806523937501096399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.887 Γ— 10⁹⁡(96-digit number)
28879209465184379942…89806523937501096401
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
5.775 Γ— 10⁹⁡(96-digit number)
57758418930368759885…79613047875002192799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.775 Γ— 10⁹⁡(96-digit number)
57758418930368759885…79613047875002192801
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
1.155 Γ— 10⁹⁢(97-digit number)
11551683786073751977…59226095750004385599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.155 Γ— 10⁹⁢(97-digit number)
11551683786073751977…59226095750004385601
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
2.310 Γ— 10⁹⁢(97-digit number)
23103367572147503954…18452191500008771199
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 242533

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 07751d62c779a53b2d578245ebccff2b54e192d35326b2a67c4cdb2b405d63d4

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 #242,533 on Chainz β†—
Circulating Supply:57,895,749 XPMΒ·at block #6,831,447 Β· updates every 60s
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