Block #163,476

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/14/2013, 12:35:12 AM · Difficulty 9.8620 · 6,646,779 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d1ed8823f9488f31e41e9daf285210bd63b7583ff8744d7d746856a145b68737

View on Chainz ↗

Height

#163,476

Difficulty

9.862045

Transactions

Size

1.61 KB

Version

Bits

09dcaef6

Nonce

141,439

Timestamp

9/14/2013, 12:35:12 AM

Confirmations

6,646,779

Mined by

⛏️ P2SHAWbm4AWfhyZEMkdPYLMs4FyYdBzNGrUw91

Merkle Root

88b7af8e5bf27b2d70343cb43d2dfa0c46030359a7a70d75f693a1a3a8711b64

Transactions (2)

Coinbase692b93d4a2eb1f…0a3c374501d789

1 in → 1 out10.2900 XPM109 B

AWbm4AWf…zNGrUw91

fe0d7c3aa99ae6…cd0abf4f480079

12 in → 2 out123.3700 XPM1.41 KB

AaZTHvEh…QXHS2iBB Aexc4U5C…VzkLuBQ9

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.

1.179 × 10⁹¹(92-digit number)

11794175819789598910…59077905359110592479

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

1.179 × 10⁹¹(92-digit number)

11794175819789598910…59077905359110592479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.179 × 10⁹¹(92-digit number)

11794175819789598910…59077905359110592481

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

2.358 × 10⁹¹(92-digit number)

23588351639579197821…18155810718221184959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.358 × 10⁹¹(92-digit number)

23588351639579197821…18155810718221184961

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

4.717 × 10⁹¹(92-digit number)

47176703279158395643…36311621436442369919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.717 × 10⁹¹(92-digit number)

47176703279158395643…36311621436442369921

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

9.435 × 10⁹¹(92-digit number)

94353406558316791287…72623242872884739839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.435 × 10⁹¹(92-digit number)

94353406558316791287…72623242872884739841

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

1.887 × 10⁹²(93-digit number)

18870681311663358257…45246485745769479679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.887 × 10⁹²(93-digit number)

18870681311663358257…45246485745769479681

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 #163,476

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