Block #457,784

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/24/2014, 3:39:46 AM · Difficulty 10.4199 · 6,356,232 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c7f3558f6a4af380428056a3139a7eab26dc8f95702c52356c22cf2d8d706d8d

View on Chainz ↗

Height

#457,784

Difficulty

10.419923

Transactions

Size

969 B

Version

Bits

0a6b8019

Nonce

415,282

Timestamp

3/24/2014, 3:39:46 AM

Confirmations

6,356,232

Mined by

AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

128b47f4652998e7bbf7e5616e2d337b6fcef023e57d42c593cb087eaf5e4bc9

Transactions (1)

Coinbase128b47f4652998…cb087eaf5e4bc9

1 in → 24 out9.2000 XPM879 B

AdFLJFhb…bsaVkAyh ASgUri65…C7NLcyBg AGz9gyZW…bo8NYQpw AMW1p9oT…2TzdaZxH AH5mD99t…Spv1yg4N

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.

5.175 × 10⁹⁴(95-digit number)

51755660601350650032…16060509910813023299

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

5.175 × 10⁹⁴(95-digit number)

51755660601350650032…16060509910813023299

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.175 × 10⁹⁴(95-digit number)

51755660601350650032…16060509910813023301

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

1.035 × 10⁹⁵(96-digit number)

10351132120270130006…32121019821626046599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.035 × 10⁹⁵(96-digit number)

10351132120270130006…32121019821626046601

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

2.070 × 10⁹⁵(96-digit number)

20702264240540260013…64242039643252093199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.070 × 10⁹⁵(96-digit number)

20702264240540260013…64242039643252093201

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

4.140 × 10⁹⁵(96-digit number)

41404528481080520026…28484079286504186399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.140 × 10⁹⁵(96-digit number)

41404528481080520026…28484079286504186401

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

8.280 × 10⁹⁵(96-digit number)

82809056962161040052…56968158573008372799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.280 × 10⁹⁵(96-digit number)

82809056962161040052…56968158573008372801

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 #457,784

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