Block #247,863

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/7/2013, 12:36:57 AM · Difficulty 9.9654 · 6,562,774 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3538c5b40b30abdfe2ea7f9069b12d7b87fd316887276f987c6e4332f4c7a259

View on Chainz ↗

Height

#247,863

Difficulty

9.965371

Transactions

Size

1.64 KB

Version

Bits

09f7228b

Nonce

178,909

Timestamp

11/7/2013, 12:36:57 AM

Confirmations

6,562,774

Mined by

⛏️ 7RzoANo4YY1xjeppLPNm9kAdtJjYCnvnsPRDSU

Merkle Root

ed2842ecdac650952012d2b66868688cc99e55386b88016910cace9064edcca6

Transactions (1)

Coinbaseed2842ecdac650…cace9064edcca6

1 in → 45 out10.0300 XPM1.55 KB

ANo4YY1x…vnsPRDSU AQtzUSwq…htAuF3yC AeNjg8HA…9AkdpcSC Ac5sZcdP…kzV4eckG AKDTDDtx…iqvw9cdY

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.

1.199 × 10¹⁰⁰(101-digit number)

11993463340354387129…97690589172243639039

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

1.199 × 10¹⁰⁰(101-digit number)

11993463340354387129…97690589172243639039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.199 × 10¹⁰⁰(101-digit number)

11993463340354387129…97690589172243639041

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

2.398 × 10¹⁰⁰(101-digit number)

23986926680708774259…95381178344487278079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.398 × 10¹⁰⁰(101-digit number)

23986926680708774259…95381178344487278081

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

4.797 × 10¹⁰⁰(101-digit number)

47973853361417548519…90762356688974556159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.797 × 10¹⁰⁰(101-digit number)

47973853361417548519…90762356688974556161

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

9.594 × 10¹⁰⁰(101-digit number)

95947706722835097039…81524713377949112319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.594 × 10¹⁰⁰(101-digit number)

95947706722835097039…81524713377949112321

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

1.918 × 10¹⁰¹(102-digit number)

19189541344567019407…63049426755898224639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.918 × 10¹⁰¹(102-digit number)

19189541344567019407…63049426755898224641

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 #247,863

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