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Block #185,097

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/29/2013, 1:50:17 AM Β· Difficulty 9.8623 Β· 6,628,910 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e3c3e93dd04f273c7eb3bc4d1aadb48092dbe3eb468d3e69b279e5bf8c4f5939
View on Chainz β†—

Height

#185,097

Difficulty

9.862260

Transactions

1

Size

200 B

Version

2

Bits

09dcbd16

Nonce

148,835

Timestamp

9/29/2013, 1:50:17 AM

Confirmations

6,628,910

Merkle Root

1b9ad8786e9eaa953c7597d348c7257de39469c85c3adf7b20df3659a95d265d
Transactions (1)
Coinbase1b9ad8786e9eaa…df3659a95d265d
1 in β†’ 1 out10.2700 XPM110 B
AFvfCa1W…3pZgbFWa
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.

3.419 Γ— 10⁹⁴(95-digit number)
34192640301181051822…38875639573725762560
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
3.419 Γ— 10⁹⁴(95-digit number)
34192640301181051822…38875639573725762559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.419 Γ— 10⁹⁴(95-digit number)
34192640301181051822…38875639573725762561
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
6.838 Γ— 10⁹⁴(95-digit number)
68385280602362103645…77751279147451525119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.838 Γ— 10⁹⁴(95-digit number)
68385280602362103645…77751279147451525121
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
1.367 Γ— 10⁹⁡(96-digit number)
13677056120472420729…55502558294903050239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.367 Γ— 10⁹⁡(96-digit number)
13677056120472420729…55502558294903050241
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
2.735 Γ— 10⁹⁡(96-digit number)
27354112240944841458…11005116589806100479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.735 Γ— 10⁹⁡(96-digit number)
27354112240944841458…11005116589806100481
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
5.470 Γ— 10⁹⁡(96-digit number)
54708224481889682916…22010233179612200959
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 185097

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 e3c3e93dd04f273c7eb3bc4d1aadb48092dbe3eb468d3e69b279e5bf8c4f5939

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 #185,097 on Chainz β†—
Circulating Supply:57,756,138 XPMΒ·at block #6,814,006 Β· updates every 60s
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