Block #158,155

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/10/2013, 4:05:50 AM · Difficulty 9.8679 · 6,659,786 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0c87919eb16e68b04d2b6e816bf9f686c7f1e0bc780d5807b222e8ca8763f193

View on Chainz ↗

Height

#158,155

Difficulty

9.867941

Transactions

Size

732 B

Version

Bits

09de3160

Nonce

421,412

Timestamp

9/10/2013, 4:05:50 AM

Confirmations

6,659,786

Mined by

⛏️ P2SHAcDi8qcNCv4YpZ2UuVgWpufZfqLGS2M3SH

Merkle Root

619677900604592cb94c64c2add6808ebefc236b6f8f4747ddf24a320ddacac5

Transactions (2)

Coinbase002f9c8cfbe8e3…47563b36dcdca6

1 in → 1 out10.2600 XPM109 B

AcDi8qcN…LGS2M3SH

349083f677d13d…38bff1a3989286

4 in → 2 out41.0800 XPM535 B

AGZvBxxa…shhkwtTn AQv4JaWu…CC7UZnbH

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.

1.460 × 10⁹¹(92-digit number)

14609338932485672744…26215672718996822719

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

1.460 × 10⁹¹(92-digit number)

14609338932485672744…26215672718996822719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.460 × 10⁹¹(92-digit number)

14609338932485672744…26215672718996822721

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

2.921 × 10⁹¹(92-digit number)

29218677864971345489…52431345437993645439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.921 × 10⁹¹(92-digit number)

29218677864971345489…52431345437993645441

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

5.843 × 10⁹¹(92-digit number)

58437355729942690979…04862690875987290879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.843 × 10⁹¹(92-digit number)

58437355729942690979…04862690875987290881

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

1.168 × 10⁹²(93-digit number)

11687471145988538195…09725381751974581759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.168 × 10⁹²(93-digit number)

11687471145988538195…09725381751974581761

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

2.337 × 10⁹²(93-digit number)

23374942291977076391…19450763503949163519

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.

★☆☆☆☆

Rarity

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #158,155

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