Block #605,022

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/28/2014, 5:36:32 AM · Difficulty 10.9100 · 6,198,454 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0edc4aa3d63fe86f6c6b83f8a476fb1ccde96ad0ed7547ad1828e8b873bb4a1c

View on Chainz ↗

Height

#605,022

Difficulty

10.909952

Transactions

Size

695 B

Version

Bits

0ae8f29a

Nonce

418,316

Timestamp

6/28/2014, 5:36:32 AM

Confirmations

6,198,454

Mined by

AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

110ec89fa7f5181f193935d9a9c072b90ab02c6f4b98f13e145e9abb1b7c8e28

Transactions (1)

Coinbase110ec89fa7f518…5e9abb1b7c8e28

1 in → 16 out8.3900 XPM607 B

AQvZBsUo…hppgRZTJ AJzWx2VD…j4ZSMit5 AJtNW28X…Syb4Ph5j AH7s8DTY…na3f76ub AebWhrRm…K61Qrkws

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.

1.469 × 10⁹⁰(91-digit number)

14695423652568820871…58869569734353231679

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

1.469 × 10⁹⁰(91-digit number)

14695423652568820871…58869569734353231679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.469 × 10⁹⁰(91-digit number)

14695423652568820871…58869569734353231681

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

2.939 × 10⁹⁰(91-digit number)

29390847305137641742…17739139468706463359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.939 × 10⁹⁰(91-digit number)

29390847305137641742…17739139468706463361

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

5.878 × 10⁹⁰(91-digit number)

58781694610275283485…35478278937412926719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.878 × 10⁹⁰(91-digit number)

58781694610275283485…35478278937412926721

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

1.175 × 10⁹¹(92-digit number)

11756338922055056697…70956557874825853439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.175 × 10⁹¹(92-digit number)

11756338922055056697…70956557874825853441

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

2.351 × 10⁹¹(92-digit number)

23512677844110113394…41913115749651706879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.351 × 10⁹¹(92-digit number)

23512677844110113394…41913115749651706881

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