Block #367,618

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/20/2014, 5:21:59 AM · Difficulty 10.4333 · 6,457,982 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

eb48bb607cc42660b352b344116db6fe9a635d21c207dd61a64a18337b6ad048

View on Chainz ↗

Height

#367,618

Difficulty

10.433304

Transactions

Size

1.01 KB

Version

Bits

0a6eecfe

Nonce

164,417

Timestamp

1/20/2014, 5:21:59 AM

Confirmations

6,457,982

Mined by

⛏️ aRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

138b3b5c1523bf77e4a7071a2a483bfce658b97444cd225394f95660c703bc6e

Transactions (1)

Coinbase138b3b5c1523bf…f95660c703bc6e

1 in → 26 out9.1700 XPM947 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 Ad9pSzHt…cpJ3y2zz AZV4TwxQ…8JnQqSoH AKR19pvT…zWLSNpj7

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.

1.347 × 10⁹⁸(99-digit number)

13474253889903674769…29577776273664952319

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

1.347 × 10⁹⁸(99-digit number)

13474253889903674769…29577776273664952319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.347 × 10⁹⁸(99-digit number)

13474253889903674769…29577776273664952321

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

2.694 × 10⁹⁸(99-digit number)

26948507779807349538…59155552547329904639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.694 × 10⁹⁸(99-digit number)

26948507779807349538…59155552547329904641

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

5.389 × 10⁹⁸(99-digit number)

53897015559614699077…18311105094659809279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.389 × 10⁹⁸(99-digit number)

53897015559614699077…18311105094659809281

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

1.077 × 10⁹⁹(100-digit number)

10779403111922939815…36622210189319618559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.077 × 10⁹⁹(100-digit number)

10779403111922939815…36622210189319618561

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

2.155 × 10⁹⁹(100-digit number)

21558806223845879631…73244420378639237119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.155 × 10⁹⁹(100-digit number)

21558806223845879631…73244420378639237121

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

4.311 × 10⁹⁹(100-digit number)

43117612447691759262…46488840757278474239

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 #367,618

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