Block #2,662,422

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/15/2018, 5:40:57 PM · Difficulty 11.6419 · 4,174,386 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ed1db5700a35db041be02d0c989935e1a864d66da0cf207520dbbc011c403c4e

View on Chainz ↗

Height

#2,662,422

Difficulty

11.641886

Transactions

Size

1.72 KB

Version

Bits

0ba452a1

Nonce

1,769,108,544

Timestamp

5/15/2018, 5:40:57 PM

Confirmations

4,174,386

Mined by

⛏️ P2SHASBYKPSNmdz5VJcyWJDpFuQx6RJXHXUqdK

Merkle Root

613dfaf5d358bde65f1a56eff16405815f74150d7ec210c41d1f05f8fb3f57ac

Transactions (2)

Coinbasef4e73662fd3d66…f0447881087d15

1 in → 1 out7.3900 XPM110 B

ASBYKPSN…JXHXUqdK

ee6a33aaa09ae5…289a5f1905e53e

10 in → 2 out37.0663 XPM1.52 KB

AYkq2NTp…ZzFjYmc6 AZ4UnHzJ…PH7NQioA

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.

1.127 × 10⁹⁷(98-digit number)

11270648468042697821…37385088527178946559

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

1.127 × 10⁹⁷(98-digit number)

11270648468042697821…37385088527178946559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.127 × 10⁹⁷(98-digit number)

11270648468042697821…37385088527178946561

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

2.254 × 10⁹⁷(98-digit number)

22541296936085395642…74770177054357893119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.254 × 10⁹⁷(98-digit number)

22541296936085395642…74770177054357893121

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

4.508 × 10⁹⁷(98-digit number)

45082593872170791284…49540354108715786239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.508 × 10⁹⁷(98-digit number)

45082593872170791284…49540354108715786241

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

9.016 × 10⁹⁷(98-digit number)

90165187744341582568…99080708217431572479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.016 × 10⁹⁷(98-digit number)

90165187744341582568…99080708217431572481

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

1.803 × 10⁹⁸(99-digit number)

18033037548868316513…98161416434863144959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.803 × 10⁹⁸(99-digit number)

18033037548868316513…98161416434863144961

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

3.606 × 10⁹⁸(99-digit number)

36066075097736633027…96322832869726289919

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 #2,662,422

Cookie Preferences