Block #497,050

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/17/2014, 9:48:30 AM · Difficulty 10.7623 · 6,306,530 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

413cedf65216e32a75012117d550fea8a064e6d267766712bb19b3bc7223dda8

View on Chainz ↗

Height

#497,050

Difficulty

10.762263

Transactions

Size

833 B

Version

Bits

0ac323af

Nonce

34,138

Timestamp

4/17/2014, 9:48:30 AM

Confirmations

6,306,530

Mined by

⛏️ aSOnAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

eed10171f5455dc02a2bae5f0928f1c063b55fc8ac6fb6df5c364ff79bf57c22

Transactions (1)

Coinbaseeed10171f5455d…364ff79bf57c22

1 in → 20 out8.6200 XPM743 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 AJtNW28X…Syb4Ph5j AWMrD5hP…ZwsoxvZ3

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.

5.592 × 10⁹⁴(95-digit number)

55922660074648328343…87326748739446467699

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

5.592 × 10⁹⁴(95-digit number)

55922660074648328343…87326748739446467699

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.592 × 10⁹⁴(95-digit number)

55922660074648328343…87326748739446467701

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

1.118 × 10⁹⁵(96-digit number)

11184532014929665668…74653497478892935399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.118 × 10⁹⁵(96-digit number)

11184532014929665668…74653497478892935401

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

2.236 × 10⁹⁵(96-digit number)

22369064029859331337…49306994957785870799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.236 × 10⁹⁵(96-digit number)

22369064029859331337…49306994957785870801

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

4.473 × 10⁹⁵(96-digit number)

44738128059718662675…98613989915571741599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.473 × 10⁹⁵(96-digit number)

44738128059718662675…98613989915571741601

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

8.947 × 10⁹⁵(96-digit number)

89476256119437325350…97227979831143483199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.947 × 10⁹⁵(96-digit number)

89476256119437325350…97227979831143483201

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