Block #506,252

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/22/2014, 11:24:40 PM · Difficulty 10.8133 · 6,285,200 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c7a76fa61553f75be09758685da1f0b1d29b60cd0d1646a7d7b06ed0cf4a3d71

View on Chainz ↗

Height

#506,252

Difficulty

10.813326

Transactions

Size

1.69 KB

Version

Bits

0ad0361e

Nonce

1,549,273

Timestamp

4/22/2014, 11:24:40 PM

Confirmations

6,285,200

Merkle Root

24f886c86aab0040dd91366ea0da88a2e459bc119f5fcded98230a02541963c5

Transactions (5)

Coinbase1a002c8cf9df72…ebd2c5f70f70eb

1 in → 1 out8.5800 XPM101 B

ASXb8Msj…BxGf64iZ

c42badc61d99b9…38365f14e94e92

1 in → 2 out8.5400 XPM226 B

AZ8yxmuh…YgMnDohN AZxkSxov…9uoWycVz

85e716011f84ef…574b7a0bc43116

1 in → 2 out8.5400 XPM227 B

AdYE6p6N…gTYqQsr4 AXwiXRiZ…Ck4yMnN7

2fc7fa5bdc89d9…72fae5f07a9e24

1 in → 2 out8.5400 XPM227 B

AS8JvVrt…S5ZaF9Dy AG8u7ddV…cU5QJSqk

45169b53cd943d…aeffed7cf2307e

5 in → 4 out9.0842 XPM856 B

AeKNrjNj…1NEq95Ta AUHFmvnF…juaRoiLd AVrzMBgN…EVKZMzxb AZH3aBJB…T7FVgZ83

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.

2.582 × 10⁹⁷(98-digit number)

25821967431006663234…00427589443039900159

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

2.582 × 10⁹⁷(98-digit number)

25821967431006663234…00427589443039900159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.582 × 10⁹⁷(98-digit number)

25821967431006663234…00427589443039900161

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

5.164 × 10⁹⁷(98-digit number)

51643934862013326469…00855178886079800319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.164 × 10⁹⁷(98-digit number)

51643934862013326469…00855178886079800321

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

1.032 × 10⁹⁸(99-digit number)

10328786972402665293…01710357772159600639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.032 × 10⁹⁸(99-digit number)

10328786972402665293…01710357772159600641

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

2.065 × 10⁹⁸(99-digit number)

20657573944805330587…03420715544319201279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.065 × 10⁹⁸(99-digit number)

20657573944805330587…03420715544319201281

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

4.131 × 10⁹⁸(99-digit number)

41315147889610661175…06841431088638402559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.131 × 10⁹⁸(99-digit number)

41315147889610661175…06841431088638402561

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