Block #523,636

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/3/2014, 5:26:34 PM · Difficulty 10.8728 · 6,290,664 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1dde8a4001369f8acb18b243f24c5a43f85a6872b750f3570342178b30e9ab7e

View on Chainz ↗

Height

#523,636

Difficulty

10.872784

Transactions

Size

732 B

Version

Bits

0adf6eca

Nonce

125,275

Timestamp

5/3/2014, 5:26:34 PM

Confirmations

6,290,664

Mined by

⛏️ taSe&AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

e3a76427002a87fe29ce8ed82ac14bdbec6877fbeeb9aafc5baea82adc062491

Transactions (1)

Coinbasee3a76427002a87…aea82adc062491

1 in → 17 out8.4500 XPM641 B

AQvZBsUo…hppgRZTJ AHwvxqCN…7z7foF67 ALfnDQkM…ExdddGtA ANNg88pG…ppn21sTe AdxPNkWD…ZMa9u34q

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.

1.765 × 10⁹⁶(97-digit number)

17654844742913732893…84642964646700780479

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

1.765 × 10⁹⁶(97-digit number)

17654844742913732893…84642964646700780479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.765 × 10⁹⁶(97-digit number)

17654844742913732893…84642964646700780481

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

3.530 × 10⁹⁶(97-digit number)

35309689485827465786…69285929293401560959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.530 × 10⁹⁶(97-digit number)

35309689485827465786…69285929293401560961

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

7.061 × 10⁹⁶(97-digit number)

70619378971654931572…38571858586803121919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.061 × 10⁹⁶(97-digit number)

70619378971654931572…38571858586803121921

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

1.412 × 10⁹⁷(98-digit number)

14123875794330986314…77143717173606243839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.412 × 10⁹⁷(98-digit number)

14123875794330986314…77143717173606243841

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

2.824 × 10⁹⁷(98-digit number)

28247751588661972628…54287434347212487679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.824 × 10⁹⁷(98-digit number)

28247751588661972628…54287434347212487681

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 #523,636

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