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Block #285,093

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/30/2013, 9:10:08 AM Β· Difficulty 9.9837 Β· 6,527,322 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6ab2b82898f71210a6bfa62b79b72a3b98c2de2defa64d0859117f8b831a2a27
View on Chainz β†—

Height

#285,093

Difficulty

9.983734

Transactions

1

Size

201 B

Version

2

Bits

09fbd602

Nonce

96,560

Timestamp

11/30/2013, 9:10:08 AM

Confirmations

6,527,322

Merkle Root

a494c2ddd96d18bc2bc727d59bfc697b832a83be0ba8b614ee165c8120df8743
Transactions (1)
Coinbasea494c2ddd96d18…165c8120df8743
1 in β†’ 1 out10.0200 XPM110 B
AeKNrjNj…1NEq95Ta
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.

1.024 Γ— 10⁹⁸(99-digit number)
10241734581622891244…23691485908558949120
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
1.024 Γ— 10⁹⁸(99-digit number)
10241734581622891244…23691485908558949119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.024 Γ— 10⁹⁸(99-digit number)
10241734581622891244…23691485908558949121
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
2.048 Γ— 10⁹⁸(99-digit number)
20483469163245782489…47382971817117898239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.048 Γ— 10⁹⁸(99-digit number)
20483469163245782489…47382971817117898241
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
4.096 Γ— 10⁹⁸(99-digit number)
40966938326491564978…94765943634235796479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.096 Γ— 10⁹⁸(99-digit number)
40966938326491564978…94765943634235796481
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
8.193 Γ— 10⁹⁸(99-digit number)
81933876652983129956…89531887268471592959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.193 Γ— 10⁹⁸(99-digit number)
81933876652983129956…89531887268471592961
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
1.638 Γ— 10⁹⁹(100-digit number)
16386775330596625991…79063774536943185919
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 285093

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 6ab2b82898f71210a6bfa62b79b72a3b98c2de2defa64d0859117f8b831a2a27

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 #285,093 on Chainz β†—
Circulating Supply:57,743,348 XPMΒ·at block #6,812,414 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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