Block #452,117

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/20/2014, 9:21:58 AM · Difficulty 10.3865 · 6,356,994 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0ca398edc1405320e03580c5644afe02544d8f23931c3a8ba4d1b41c345f17dc

View on Chainz ↗

Height

#452,117

Difficulty

10.386480

Transactions

Size

969 B

Version

Bits

0a62f058

Nonce

90,817

Timestamp

3/20/2014, 9:21:58 AM

Confirmations

6,356,994

Mined by

⛏️ aS*2AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

70138f9ba48ec14573dcd3dd48fe50e9c4121c1fadd7650f38fe62b4a4df7efb

Transactions (1)

Coinbase70138f9ba48ec1…fe62b4a4df7efb

1 in → 24 out9.2600 XPM879 B

AQvZBsUo…hppgRZTJ AScAzqGc…BZ6tV1vJ ALqxX1WA…hsKjbnXn AdhWfaX2…aX7YvEJq 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.

1.857 × 10⁹⁵(96-digit number)

18577280719529647097…60154572626115381759

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

1.857 × 10⁹⁵(96-digit number)

18577280719529647097…60154572626115381759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.857 × 10⁹⁵(96-digit number)

18577280719529647097…60154572626115381761

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

3.715 × 10⁹⁵(96-digit number)

37154561439059294195…20309145252230763519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.715 × 10⁹⁵(96-digit number)

37154561439059294195…20309145252230763521

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

7.430 × 10⁹⁵(96-digit number)

74309122878118588391…40618290504461527039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.430 × 10⁹⁵(96-digit number)

74309122878118588391…40618290504461527041

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

1.486 × 10⁹⁶(97-digit number)

14861824575623717678…81236581008923054079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.486 × 10⁹⁶(97-digit number)

14861824575623717678…81236581008923054081

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

2.972 × 10⁹⁶(97-digit number)

29723649151247435356…62473162017846108159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.972 × 10⁹⁶(97-digit number)

29723649151247435356…62473162017846108161

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 #452,117

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