Block #246,492

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/6/2013, 4:12:32 AM · Difficulty 9.9643 · 6,562,431 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

62d8bfd0f6f8477bc6f551d9db267eb7260b09cdabb341e7745548a0986200c8

View on Chainz ↗

Height

#246,492

Difficulty

9.964291

Transactions

Size

2.17 KB

Version

Bits

09f6dbce

Nonce

4,311

Timestamp

11/6/2013, 4:12:32 AM

Confirmations

6,562,431

Mined by

⛏️ RyALdHh27brbEqnGMrZaaR18HaaAXNbqrvPf

Merkle Root

9146e30dbe08091e69857e5e54af0335b61462c2d6b5cd596fb0ebff11122fc6

Transactions (1)

Coinbase9146e30dbe0809…b0ebff11122fc6

1 in → 61 out10.0300 XPM2.09 KB

ALdHh27b…XNbqrvPf ANpPrsJp…YzdEphWb AQpfNnGB…JfWDSzmH ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC

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.

1.345 × 10⁹⁷(98-digit number)

13458422088346097645…18709437075778321019

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

1.345 × 10⁹⁷(98-digit number)

13458422088346097645…18709437075778321019

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.345 × 10⁹⁷(98-digit number)

13458422088346097645…18709437075778321021

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

2.691 × 10⁹⁷(98-digit number)

26916844176692195291…37418874151556642039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.691 × 10⁹⁷(98-digit number)

26916844176692195291…37418874151556642041

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

5.383 × 10⁹⁷(98-digit number)

53833688353384390582…74837748303113284079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.383 × 10⁹⁷(98-digit number)

53833688353384390582…74837748303113284081

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

1.076 × 10⁹⁸(99-digit number)

10766737670676878116…49675496606226568159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.076 × 10⁹⁸(99-digit number)

10766737670676878116…49675496606226568161

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

2.153 × 10⁹⁸(99-digit number)

21533475341353756233…99350993212453136319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.153 × 10⁹⁸(99-digit number)

21533475341353756233…99350993212453136321

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

4.306 × 10⁹⁸(99-digit number)

43066950682707512466…98701986424906272639

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #246,492

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