Block #2,207,457

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/15/2017, 6:30:03 AM · Difficulty 10.9454 · 4,634,846 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7387d3c82982e7d7cfc8d291c242a8c71a250440a51e370cc53ff3a5462736a3

View on Chainz ↗

Height

#2,207,457

Difficulty

10.945390

Transactions

Size

425 B

Version

Bits

0af2050d

Nonce

1,070,647,670

Timestamp

7/15/2017, 6:30:03 AM

Confirmations

4,634,846

Mined by

⛏️ P2SHAJA6hBqy9k7i3uH9A4CnKLdyfSTEvUCCsr

Merkle Root

dd9deeadcefbc9cf09c02fe7957ef19c664487ca9b5e23d0993e0329172e76a5

Transactions (2)

Coinbasec8f3fb6f7188bf…b7f13ee064971b

1 in → 1 out8.3400 XPM110 B

AJA6hBqy…TEvUCCsr

7f71cca7d7a125…a37aa657d0e358

1 in → 2 out26842.6280 XPM225 B

AMNqyy2W…ise9w8w1 AL8edQDg…zCracPvv

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.

6.301 × 10⁹⁵(96-digit number)

63015357656132503143…35124826079202963839

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

6.301 × 10⁹⁵(96-digit number)

63015357656132503143…35124826079202963839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.301 × 10⁹⁵(96-digit number)

63015357656132503143…35124826079202963841

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

1.260 × 10⁹⁶(97-digit number)

12603071531226500628…70249652158405927679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.260 × 10⁹⁶(97-digit number)

12603071531226500628…70249652158405927681

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

2.520 × 10⁹⁶(97-digit number)

25206143062453001257…40499304316811855359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.520 × 10⁹⁶(97-digit number)

25206143062453001257…40499304316811855361

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

5.041 × 10⁹⁶(97-digit number)

50412286124906002514…80998608633623710719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.041 × 10⁹⁶(97-digit number)

50412286124906002514…80998608633623710721

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

1.008 × 10⁹⁷(98-digit number)

10082457224981200502…61997217267247421439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.008 × 10⁹⁷(98-digit number)

10082457224981200502…61997217267247421441

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

2.016 × 10⁹⁷(98-digit number)

20164914449962401005…23994434534494842879

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 #2,207,457

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