Block #495,068

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/16/2014, 11:23:07 AM · Difficulty 10.7302 · 6,299,806 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

985186dc3ac55d2960db6c79246c70a180b3241ff11484e6cb47b72762a01698

View on Chainz ↗

Height

#495,068

Difficulty

10.730210

Transactions

Size

28.75 KB

Version

Bits

0abaef09

Nonce

29,747,384

Timestamp

4/16/2014, 11:23:07 AM

Confirmations

6,299,806

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

7535873128ec345ef47a4d7da391b8763119c1413725f69e86f341bbb1576cec

Transactions (4)

Coinbase758b4d6b3b4bad…f71c3984d3947d

1 in → 1 out8.9800 XPM116 B

AbwWkWZt…kawDhufa

28835dd83d8e9e…db0cbe04aec8e9

193 in → 2 out483.6454 XPM27.96 KB

ATkAj878…iU3UKp2W ALz3P4sN…ULz9YPrk

cab3870f30e806…f1bb056b7a2893

1 in → 2 out3.1002 XPM226 B

AJs6Ps4B…gVqJMFFr AQYfM6tR…wtD7VsKo

59fd4934ff7a8f…23a5d8b360be38

2 in → 2 out0.5518 XPM375 B

AQ236kx1…SA7ixpmc ATFY9TZ5…pqx4GsPx

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.

7.594 × 10⁹⁷(98-digit number)

75942315474635164191…98631818249744907799

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

7.594 × 10⁹⁷(98-digit number)

75942315474635164191…98631818249744907799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.594 × 10⁹⁷(98-digit number)

75942315474635164191…98631818249744907801

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

1.518 × 10⁹⁸(99-digit number)

15188463094927032838…97263636499489815599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.518 × 10⁹⁸(99-digit number)

15188463094927032838…97263636499489815601

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

3.037 × 10⁹⁸(99-digit number)

30376926189854065676…94527272998979631199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.037 × 10⁹⁸(99-digit number)

30376926189854065676…94527272998979631201

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

6.075 × 10⁹⁸(99-digit number)

60753852379708131353…89054545997959262399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.075 × 10⁹⁸(99-digit number)

60753852379708131353…89054545997959262401

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

1.215 × 10⁹⁹(100-digit number)

12150770475941626270…78109091995918524799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.215 × 10⁹⁹(100-digit number)

12150770475941626270…78109091995918524801

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