Block #161,294

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/12/2013, 1:59:21 PM · Difficulty 9.8590 · 6,646,632 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3c6e2b936cad175c3c90365ec9755c99510734b9c2301b5673bde29b3090e0e6

View on Chainz ↗

Height

#161,294

Difficulty

9.858987

Transactions

Size

471 B

Version

Bits

09dbe69a

Nonce

70,148

Timestamp

9/12/2013, 1:59:21 PM

Confirmations

6,646,632

Mined by

⛏️ P2SHAenheVbJZmADSsB5ffYM4Fy4hJsEEpRhLA

Merkle Root

618a73cdf1d3932aaf0c2a8c1543b4da3aac533ab18eef5f26764010bae68680

Transactions (2)

Coinbased092c468a894fa…e750143efe3887

1 in → 1 out10.2800 XPM109 B

AenheVbJ…sEEpRhLA

ec75de720b9c2b…078c21029616be

2 in → 1 out20.4900 XPM272 B

AMF6scky…ugQApVzx

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.

1.627 × 10⁹⁵(96-digit number)

16273423482743036332…04404017822939836799

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

1.627 × 10⁹⁵(96-digit number)

16273423482743036332…04404017822939836799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.627 × 10⁹⁵(96-digit number)

16273423482743036332…04404017822939836801

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

3.254 × 10⁹⁵(96-digit number)

32546846965486072664…08808035645879673599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.254 × 10⁹⁵(96-digit number)

32546846965486072664…08808035645879673601

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

6.509 × 10⁹⁵(96-digit number)

65093693930972145329…17616071291759347199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.509 × 10⁹⁵(96-digit number)

65093693930972145329…17616071291759347201

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

1.301 × 10⁹⁶(97-digit number)

13018738786194429065…35232142583518694399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.301 × 10⁹⁶(97-digit number)

13018738786194429065…35232142583518694401

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

2.603 × 10⁹⁶(97-digit number)

26037477572388858131…70464285167037388799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.603 × 10⁹⁶(97-digit number)

26037477572388858131…70464285167037388801

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

Block #161,294

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