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Block #185,519

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/29/2013, 8:55:43 AM · Difficulty 9.8621 · 6,605,994 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e0099e7677389e4fdf354ab39d8fca3268a5a175e92f213db5b38e288e5250cf

View on Chainz ↗

Height

#185,519

Difficulty

9.862136

Transactions

Size

605 B

Version

Bits

09dcb4fa

Nonce

1,770

Timestamp

9/29/2013, 8:55:43 AM

Confirmations

6,605,994

Merkle Root

e434c0a12257f40d9d1994c6bda7f6b19d22dc02d55c36841b9bb5b9310b75f7

Transactions (2)

Coinbase0b401467325a9c…1c39626a30d6ef

1 in → 1 out10.2800 XPM109 B

ASM8MtFz…mPpwdSdZ

3e12a1717f7807…4504becb9557a0

2 in → 5 out20.5500 XPM406 B

ANvtpRa1…QjsraDJz AeckU1Kq…a9chH61d ARTJCDz1…oJ6Hi1d9 AGdYdg5f…ZrePPako AQXUSoBL…CzbjKp8b

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

4.721 × 10⁹³(94-digit number)

47219040228400913451…91072141821052423960

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

4.721 × 10⁹³(94-digit number)

47219040228400913451…91072141821052423959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.721 × 10⁹³(94-digit number)

47219040228400913451…91072141821052423961

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

9.443 × 10⁹³(94-digit number)

94438080456801826903…82144283642104847919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.443 × 10⁹³(94-digit number)

94438080456801826903…82144283642104847921

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.888 × 10⁹⁴(95-digit number)

18887616091360365380…64288567284209695839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.888 × 10⁹⁴(95-digit number)

18887616091360365380…64288567284209695841

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

3.777 × 10⁹⁴(95-digit number)

37775232182720730761…28577134568419391679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.777 × 10⁹⁴(95-digit number)

37775232182720730761…28577134568419391681

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

7.555 × 10⁹⁴(95-digit number)

75550464365441461522…57154269136838783359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.555 × 10⁹⁴(95-digit number)

75550464365441461522…57154269136838783361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

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 — the large number shown above — 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 →

★★☆☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 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 185519

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 e0099e7677389e4fdf354ab39d8fca3268a5a175e92f213db5b38e288e5250cf

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 → Debug Window → 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 #185,519 on Chainz ↗