Block #507,308

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/23/2014, 3:53:56 PM · Difficulty 10.8159 · 6,288,188 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

029ed72a5ccd9568add2ae1c1b095c8551c3fcd440dd80bf0c2e47de1b33620e

View on Chainz ↗

Height

#507,308

Difficulty

10.815882

Transactions

Size

801 B

Version

Bits

0ad0dda8

Nonce

3,014

Timestamp

4/23/2014, 3:53:56 PM

Confirmations

6,288,188

Mined by

⛏️ aSWAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

964b0acd3a4cee75e1ef8d90d85b6f549aafa7a55717cd35463a5a7855367183

Transactions (1)

Coinbase964b0acd3a4cee…3a5a7855367183

1 in → 19 out8.5300 XPM709 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AdxPNkWD…ZMa9u34q ATKK7iFz…wZm46KN1 AJtNW28X…Syb4Ph5j

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.

2.002 × 10¹⁰⁰(101-digit number)

20025631732368104471…24794686881122515199

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

2.002 × 10¹⁰⁰(101-digit number)

20025631732368104471…24794686881122515199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.002 × 10¹⁰⁰(101-digit number)

20025631732368104471…24794686881122515201

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

4.005 × 10¹⁰⁰(101-digit number)

40051263464736208943…49589373762245030399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.005 × 10¹⁰⁰(101-digit number)

40051263464736208943…49589373762245030401

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

8.010 × 10¹⁰⁰(101-digit number)

80102526929472417886…99178747524490060799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.010 × 10¹⁰⁰(101-digit number)

80102526929472417886…99178747524490060801

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

1.602 × 10¹⁰¹(102-digit number)

16020505385894483577…98357495048980121599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.602 × 10¹⁰¹(102-digit number)

16020505385894483577…98357495048980121601

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

3.204 × 10¹⁰¹(102-digit number)

32041010771788967154…96714990097960243199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.204 × 10¹⁰¹(102-digit number)

32041010771788967154…96714990097960243201

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