Block #100,452

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/6/2013, 4:33:14 AM · Difficulty 9.4252 · 6,697,360 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

79176ec8ffba1bce4e69f02e3b652f5aeed4479de4d2792d72fbf3f1d025d61d

View on Chainz ↗

Height

#100,452

Difficulty

9.425152

Transactions

Size

782 B

Version

Bits

096cd6c7

Nonce

113,958

Timestamp

8/6/2013, 4:33:14 AM

Confirmations

6,697,360

Mined by

⛏️ P2SHAMqtGnyAG4UWLzHrTHFmwbhGkmv6wFYAGv

Merkle Root

e0175f8436e08ff7e5567d1cc7e79ff96b45bcc99c145e70b3d789c3ddd3afe4

Transactions (4)

Coinbase9a390401504a59…63b42fbb3319e3

1 in → 1 out11.2700 XPM109 B

AMqtGnyA…v6wFYAGv

6eca198c901d6e…bc0459d26e1914

1 in → 2 out11.5600 XPM192 B

AWqrmbWo…ZcSjTJTw ALJbFeev…aXFynP3K

8466a614f467e6…5eea31cff40877

1 in → 2 out11.5700 XPM191 B

AG32NJPb…ZTSKeTzu AaMRUFMG…S11BNFrC

db02f0113ad477…c1e4be88e3d9cc

1 in → 1 out5.7800 XPM192 B

AeguK5Ai…CLUqoF9q

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.

5.857 × 10¹¹⁴(115-digit number)

58578285037441906529…02646751497753176469

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

5.857 × 10¹¹⁴(115-digit number)

58578285037441906529…02646751497753176469

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.857 × 10¹¹⁴(115-digit number)

58578285037441906529…02646751497753176471

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

1.171 × 10¹¹⁵(116-digit number)

11715657007488381305…05293502995506352939

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.171 × 10¹¹⁵(116-digit number)

11715657007488381305…05293502995506352941

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

2.343 × 10¹¹⁵(116-digit number)

23431314014976762611…10587005991012705879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.343 × 10¹¹⁵(116-digit number)

23431314014976762611…10587005991012705881

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

4.686 × 10¹¹⁵(116-digit number)

46862628029953525223…21174011982025411759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.686 × 10¹¹⁵(116-digit number)

46862628029953525223…21174011982025411761

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

9.372 × 10¹¹⁵(116-digit number)

93725256059907050446…42348023964050823519

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