Block #455,871

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/22/2014, 7:58:24 PM · Difficulty 10.4172 · 6,360,707 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fec3d838b8a761560e1945600d1b4725b64575ef09965bd594a3f498db581083

View on Chainz ↗

Height

#455,871

Difficulty

10.417212

Transactions

Size

936 B

Version

Bits

0a6ace63

Nonce

66,074

Timestamp

3/22/2014, 7:58:24 PM

Confirmations

6,360,707

Mined by

⛏️ |kAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

fcf32f903f9f52edb2cb3af8beafb02cf0783e44e3b7d08a18ac6727c9e436db

Transactions (1)

Coinbasefcf32f903f9f52…ac6727c9e436db

1 in → 23 out9.2000 XPM845 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw ATp4jJhs…TbSgR8Qb ASgUri65…C7NLcyBg AJ6RXmZG…A2yg7Qhr

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.

1.251 × 10⁹⁶(97-digit number)

12518108385015991774…92559462987911635199

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

1.251 × 10⁹⁶(97-digit number)

12518108385015991774…92559462987911635199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.251 × 10⁹⁶(97-digit number)

12518108385015991774…92559462987911635201

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

2.503 × 10⁹⁶(97-digit number)

25036216770031983548…85118925975823270399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.503 × 10⁹⁶(97-digit number)

25036216770031983548…85118925975823270401

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

5.007 × 10⁹⁶(97-digit number)

50072433540063967097…70237851951646540799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.007 × 10⁹⁶(97-digit number)

50072433540063967097…70237851951646540801

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

1.001 × 10⁹⁷(98-digit number)

10014486708012793419…40475703903293081599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.001 × 10⁹⁷(98-digit number)

10014486708012793419…40475703903293081601

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

2.002 × 10⁹⁷(98-digit number)

20028973416025586838…80951407806586163199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.002 × 10⁹⁷(98-digit number)

20028973416025586838…80951407806586163201

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 #455,871

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