Block #134,209

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/25/2013, 10:41:35 PM · Difficulty 9.8014 · 6,655,779 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

6,655,779

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…55589447274381668799

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.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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

Cross-reference on Chainz Explorer