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Block #182,591

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/27/2013, 10:37:12 AM Β· Difficulty 9.8575 Β· 6,630,136 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
00e04e75321f02c4c257da87cb4070a59529ffb05db12a98dd4fcb2bae0efe9c
View on Chainz β†—

Height

#182,591

Difficulty

9.857500

Transactions

1

Size

199 B

Version

2

Bits

09db851f

Nonce

8,301

Timestamp

9/27/2013, 10:37:12 AM

Confirmations

6,630,136

Merkle Root

5e730900b5c807a8b0393b9016e5d35d546fbe8e2b5cfb40894e862964bbc486
Transactions (1)
Coinbase5e730900b5c807…4e862964bbc486
1 in β†’ 1 out10.2800 XPM110 B
ANvtpRa1…QjsraDJz
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.

2.055 Γ— 10⁹²(93-digit number)
20557305580112092472…89485720225136745910
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
2.055 Γ— 10⁹²(93-digit number)
20557305580112092472…89485720225136745909
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.055 Γ— 10⁹²(93-digit number)
20557305580112092472…89485720225136745911
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
4.111 Γ— 10⁹²(93-digit number)
41114611160224184944…78971440450273491819
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.111 Γ— 10⁹²(93-digit number)
41114611160224184944…78971440450273491821
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
8.222 Γ— 10⁹²(93-digit number)
82229222320448369889…57942880900546983639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.222 Γ— 10⁹²(93-digit number)
82229222320448369889…57942880900546983641
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
1.644 Γ— 10⁹³(94-digit number)
16445844464089673977…15885761801093967279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.644 Γ— 10⁹³(94-digit number)
16445844464089673977…15885761801093967281
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
3.289 Γ— 10⁹³(94-digit number)
32891688928179347955…31771523602187934559
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 182591

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 00e04e75321f02c4c257da87cb4070a59529ffb05db12a98dd4fcb2bae0efe9c

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 #182,591 on Chainz β†—
Circulating Supply:57,745,856 XPMΒ·at block #6,812,726 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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