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Block #234,301

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/30/2013, 6:05:37 AM Β· Difficulty 9.9438 Β· 6,560,733 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f9d8193c94b5c29af2cc5c12f1aa091e7601e2a2247443d1ca96ea1202fc22ad
View on Chainz β†—

Height

#234,301

Difficulty

9.943826

Transactions

1

Size

204 B

Version

2

Bits

09f19e98

Nonce

186,821

Timestamp

10/30/2013, 6:05:37 AM

Confirmations

6,560,733

Merkle Root

01675fa2b2da6bdcc1b5eb62be159520f0cce66adb490600f813722e23454a45
Transactions (1)
Coinbase01675fa2b2da6b…13722e23454a45
1 in β†’ 1 out10.1000 XPM116 B
AcLBm5Z9…S683d7c3
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.

7.238 Γ— 10⁹⁰(91-digit number)
72388582226758355667…72943159023319726080
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
7.238 Γ— 10⁹⁰(91-digit number)
72388582226758355667…72943159023319726079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.238 Γ— 10⁹⁰(91-digit number)
72388582226758355667…72943159023319726081
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
1.447 Γ— 10⁹¹(92-digit number)
14477716445351671133…45886318046639452159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.447 Γ— 10⁹¹(92-digit number)
14477716445351671133…45886318046639452161
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
2.895 Γ— 10⁹¹(92-digit number)
28955432890703342267…91772636093278904319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.895 Γ— 10⁹¹(92-digit number)
28955432890703342267…91772636093278904321
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
5.791 Γ— 10⁹¹(92-digit number)
57910865781406684534…83545272186557808639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.791 Γ— 10⁹¹(92-digit number)
57910865781406684534…83545272186557808641
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
1.158 Γ— 10⁹²(93-digit number)
11582173156281336906…67090544373115617279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.158 Γ— 10⁹²(93-digit number)
11582173156281336906…67090544373115617281
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 234301

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 f9d8193c94b5c29af2cc5c12f1aa091e7601e2a2247443d1ca96ea1202fc22ad

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 #234,301 on Chainz β†—
Circulating Supply:57,604,313 XPMΒ·at block #6,795,033 Β· updates every 60s
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