Block #100,454

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/6/2013, 4:35:48 AM · Difficulty 9.4250 · 6,706,645 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2e74e29a761b82d2c8a0d61855ca27ad94766b50f33f93db36de8a46ec9033f9

View on Chainz ↗

Height

#100,454

Difficulty

9.425050

Transactions

Size

208 B

Version

Bits

096cd00f

Nonce

267,419

Timestamp

8/6/2013, 4:35:48 AM

Confirmations

6,706,645

Mined by

⛏️ P2SHAT5A2KL6kAm5Pa3anhC8W4LVscCT16n6i2

Merkle Root

7b0a1b1f3f7c414a7ed175f38e7caabc3fd99059f9a67f5a10fe4d92af9f2a95

Transactions (1)

Coinbase7b0a1b1f3f7c41…fe4d92af9f2a95

1 in → 1 out11.2400 XPM112 B

AT5A2KL6…CT16n6i2

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.

1.557 × 10¹⁰⁹(110-digit number)

15575494446168746188…60501544788954545919

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

1.557 × 10¹⁰⁹(110-digit number)

15575494446168746188…60501544788954545919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.557 × 10¹⁰⁹(110-digit number)

15575494446168746188…60501544788954545921

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

3.115 × 10¹⁰⁹(110-digit number)

31150988892337492377…21003089577909091839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.115 × 10¹⁰⁹(110-digit number)

31150988892337492377…21003089577909091841

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

6.230 × 10¹⁰⁹(110-digit number)

62301977784674984754…42006179155818183679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.230 × 10¹⁰⁹(110-digit number)

62301977784674984754…42006179155818183681

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

1.246 × 10¹¹⁰(111-digit number)

12460395556934996950…84012358311636367359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.246 × 10¹¹⁰(111-digit number)

12460395556934996950…84012358311636367361

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

2.492 × 10¹¹⁰(111-digit number)

24920791113869993901…68024716623272734719

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 #100,454

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