Block #531,316

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/8/2014, 10:35:05 AM · Difficulty 10.8938 · 6,295,406 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

86ad3312b4ffeb5e79baf03211dff60c6e9b99c378e5b719611fed97f4fe2296

View on Chainz ↗

Height

#531,316

Difficulty

10.893770

Transactions

Size

561 B

Version

Bits

0ae4ce1e

Nonce

147,542

Timestamp

5/8/2014, 10:35:05 AM

Confirmations

6,295,406

Mined by

⛏️ taSkAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

9e8a5181b069c02cde680829c95d91b7d78237ab44d91746e9b474bded50db2e

Transactions (1)

Coinbase9e8a5181b069c0…b474bded50db2e

1 in → 12 out8.4100 XPM471 B

AQvZBsUo…hppgRZTJ AdxPNkWD…ZMa9u34q AUbecsVa…i8zo8qRf AJtNW28X…Syb4Ph5j AJzWx2VD…j4ZSMit5

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.

5.772 × 10⁹⁴(95-digit number)

57722736373314658100…34986493630667295999

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

5.772 × 10⁹⁴(95-digit number)

57722736373314658100…34986493630667295999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.772 × 10⁹⁴(95-digit number)

57722736373314658100…34986493630667296001

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

1.154 × 10⁹⁵(96-digit number)

11544547274662931620…69972987261334591999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.154 × 10⁹⁵(96-digit number)

11544547274662931620…69972987261334592001

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

2.308 × 10⁹⁵(96-digit number)

23089094549325863240…39945974522669183999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.308 × 10⁹⁵(96-digit number)

23089094549325863240…39945974522669184001

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

4.617 × 10⁹⁵(96-digit number)

46178189098651726480…79891949045338367999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.617 × 10⁹⁵(96-digit number)

46178189098651726480…79891949045338368001

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

9.235 × 10⁹⁵(96-digit number)

92356378197303452960…59783898090676735999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.235 × 10⁹⁵(96-digit number)

92356378197303452960…59783898090676736001

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 #531,316

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