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Block #135,639

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/26/2013, 6:03:26 PM · Difficulty 9.8119 · 6,678,375 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

55ae343fcd251acc80ed0d2ec97a27cd72ef2c4107a892ed49955d122e8096cb

View on Chainz ↗

Height

#135,639

Difficulty

9.811851

Transactions

Size

571 B

Version

Bits

09cfd573

Nonce

189,296

Timestamp

8/26/2013, 6:03:26 PM

Confirmations

6,678,375

Merkle Root

7d31ce423a765b9c3f1e9927d19dba52502de68f354b844fbb3ea326ebdc749a

Transactions (2)

Coinbase51a5a366724769…39b98375dc90c8

1 in → 1 out10.3800 XPM109 B

AVJaZtXC…gGZDZ3Yk

6037928ba82863…ea0103079ffe6e

2 in → 2 out24.2300 XPM373 B

AGaLmxcV…g7Rj6VfZ AcFMSKzj…PVg8XeoV

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.

2.685 × 10⁹²(93-digit number)

26856098683779702690…60394509525932471040

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

2.685 × 10⁹²(93-digit number)

26856098683779702690…60394509525932471039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.685 × 10⁹²(93-digit number)

26856098683779702690…60394509525932471041

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

5.371 × 10⁹²(93-digit number)

53712197367559405381…20789019051864942079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.371 × 10⁹²(93-digit number)

53712197367559405381…20789019051864942081

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

1.074 × 10⁹³(94-digit number)

10742439473511881076…41578038103729884159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.074 × 10⁹³(94-digit number)

10742439473511881076…41578038103729884161

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

2.148 × 10⁹³(94-digit number)

21484878947023762152…83156076207459768319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.148 × 10⁹³(94-digit number)

21484878947023762152…83156076207459768321

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

4.296 × 10⁹³(94-digit number)

42969757894047524305…66312152414919536639

Verify on FactorDB ↗Wolfram Alpha ↗

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 — 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

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 × 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 135639

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 55ae343fcd251acc80ed0d2ec97a27cd72ef2c4107a892ed49955d122e8096cb

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 #135,639 on Chainz ↗

Block #135,639

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