Block #473,810

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/4/2014, 4:27:17 AM · Difficulty 10.4452 · 6,334,101 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

727f28af7b3cffba4d3836aa8143dc288d8023dad0a08305e4a509b396e531ef

View on Chainz ↗

Height

#473,810

Difficulty

10.445227

Transactions

Size

935 B

Version

Bits

0a71fa64

Nonce

166,229

Timestamp

4/4/2014, 4:27:17 AM

Confirmations

6,334,101

Mined by

⛏️ :aS>4AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

5fb89d7d033b482513c700efc417c050bc2079a5a7b842c6f48625bc4ef8595f

Transactions (1)

Coinbase5fb89d7d033b48…8625bc4ef8595f

1 in → 23 out9.1500 XPM845 B

AQvZBsUo…hppgRZTJ AYA1NRP5…dGfAwNqr ANNg88pG…ppn21sTe AQ8QAT3J…rCFKuVbR ATKK7iFz…wZm46KN1

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.

1.002 × 10⁹⁵(96-digit number)

10025727896813668534…95333395195134947299

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

1.002 × 10⁹⁵(96-digit number)

10025727896813668534…95333395195134947299

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.002 × 10⁹⁵(96-digit number)

10025727896813668534…95333395195134947301

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

2.005 × 10⁹⁵(96-digit number)

20051455793627337069…90666790390269894599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.005 × 10⁹⁵(96-digit number)

20051455793627337069…90666790390269894601

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

4.010 × 10⁹⁵(96-digit number)

40102911587254674138…81333580780539789199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.010 × 10⁹⁵(96-digit number)

40102911587254674138…81333580780539789201

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

8.020 × 10⁹⁵(96-digit number)

80205823174509348276…62667161561079578399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.020 × 10⁹⁵(96-digit number)

80205823174509348276…62667161561079578401

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

1.604 × 10⁹⁶(97-digit number)

16041164634901869655…25334323122159156799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.604 × 10⁹⁶(97-digit number)

16041164634901869655…25334323122159156801

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

Block #473,810

Cookie Preferences