Block #99,903

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/5/2013, 9:59:32 PM · Difficulty 9.4061 · 6,708,525 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

82de338e781a0f82efa1402d715428dbaddf014822c65e31cc1282d7bca140b4

View on Chainz ↗

Height

#99,903

Difficulty

9.406115

Transactions

Size

205 B

Version

Bits

0967f726

Nonce

42,394

Timestamp

8/5/2013, 9:59:32 PM

Confirmations

6,708,525

Mined by

⛏️ P2SHAHpT5Ubr7tyJrMtf8YgCHZoPSbErRZ8yTA

Merkle Root

7ad2467e7f403ff767a5c3da80b2e716c2412fa90a77e67cda9651f81308ee6e

Transactions (1)

Coinbase7ad2467e7f403f…9651f81308ee6e

1 in → 1 out11.2900 XPM109 B

AHpT5Ubr…ErRZ8yTA

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.

1.041 × 10¹¹⁰(111-digit number)

10419810738970838725…72327489307418310239

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

1.041 × 10¹¹⁰(111-digit number)

10419810738970838725…72327489307418310239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.041 × 10¹¹⁰(111-digit number)

10419810738970838725…72327489307418310241

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

2.083 × 10¹¹⁰(111-digit number)

20839621477941677451…44654978614836620479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.083 × 10¹¹⁰(111-digit number)

20839621477941677451…44654978614836620481

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

4.167 × 10¹¹⁰(111-digit number)

41679242955883354903…89309957229673240959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.167 × 10¹¹⁰(111-digit number)

41679242955883354903…89309957229673240961

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

8.335 × 10¹¹⁰(111-digit number)

83358485911766709807…78619914459346481919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.335 × 10¹¹⁰(111-digit number)

83358485911766709807…78619914459346481921

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

1.667 × 10¹¹¹(112-digit number)

16671697182353341961…57239828918692963839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.667 × 10¹¹¹(112-digit number)

16671697182353341961…57239828918692963841

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 #99,903

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