Home/Chain Registry/Block #134,209

Block #134,209

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/25/2013, 10:41:35 PM · Difficulty 9.8014 · 6,661,755 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3fdaa722d17bec7b7bb4d08fe8098a09a8101ea87b41c68579b3daaebf87edae

View on Chainz ↗

Height

#134,209

Difficulty

9.801438

Transactions

Size

1.69 KB

Version

Bits

09cd2b11

Nonce

36,369

Timestamp

8/25/2013, 10:41:35 PM

Confirmations

6,661,755

Merkle Root

78507e3ae143b899f9dae8949ddaf7ab4e82ffda0968486be61f14cb61c82c58

Transactions (3)

Coinbase24873ad6709ada…85ab6aac45a9c9

1 in → 1 out10.4200 XPM109 B

AY3Rt1ex…GJoFTK6u

5b596e056bc5e6…06e64da2e0c948

1 in → 1 out10.4700 XPM158 B

AYHMpEjc…yr7fFvHC

b838f470950a9d…01e24b06d7bc70

9 in → 1 out20.6432 XPM1.34 KB

APBxWs9R…KTHWo3fT

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.

2.957 × 10⁹²(93-digit number)

29578742586024994422…55589447274381668800

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

2.957 × 10⁹²(93-digit number)

29578742586024994422…55589447274381668799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.957 × 10⁹²(93-digit number)

29578742586024994422…55589447274381668801

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

5.915 × 10⁹²(93-digit number)

59157485172049988845…11178894548763337599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.915 × 10⁹²(93-digit number)

59157485172049988845…11178894548763337601

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

1.183 × 10⁹³(94-digit number)

11831497034409997769…22357789097526675199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.183 × 10⁹³(94-digit number)

11831497034409997769…22357789097526675201

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

2.366 × 10⁹³(94-digit number)

23662994068819995538…44715578195053350399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.366 × 10⁹³(94-digit number)

23662994068819995538…44715578195053350401

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

4.732 × 10⁹³(94-digit number)

47325988137639991076…89431156390106700799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.732 × 10⁹³(94-digit number)

47325988137639991076…89431156390106700801

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 134209

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 3fdaa722d17bec7b7bb4d08fe8098a09a8101ea87b41c68579b3daaebf87edae

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 #134,209 on Chainz ↗