Block #500,606

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/19/2014, 6:14:19 AM · Difficulty 10.8012 · 6,308,699 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3417946f2fad3c84824b38dfa96c05964a0817a3df8bcff80aceb76733296e6f

View on Chainz ↗

Height

#500,606

Difficulty

10.801213

Transactions

Size

885 B

Version

Bits

0acd1c4f

Nonce

84,243,720

Timestamp

4/19/2014, 6:14:19 AM

Confirmations

6,308,699

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

4f96f4ee5f2523add70ef52476ce68ac1ec211963fb8a8cf9c46b379cb3e43d1

Transactions (4)

Coinbase77845561f3970b…d216db4457c3f2

1 in → 1 out8.5900 XPM116 B

AbwWkWZt…kawDhufa

0ccce1ab530033…1cfbd73c9f18f6

1 in → 2 out8.0734 XPM226 B

AL9z5FfD…SzSf9kb5 ANCo6waC…DqFmvW51

42970b5ed36c0f…474b1cc79a964a

1 in → 2 out7.5900 XPM225 B

AM8GuxnN…AfjbhWoV AHEHX5wJ…9DyyTtk6

29b77be95ebb19…c6eda6bff4162d

1 in → 2 out7.0786 XPM227 B

AV4pZheo…Vh61p9bS AQGegLKo…io3H8qqD

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.

3.795 × 10⁹⁷(98-digit number)

37951135084618324946…11491297613153873279

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

3.795 × 10⁹⁷(98-digit number)

37951135084618324946…11491297613153873279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.795 × 10⁹⁷(98-digit number)

37951135084618324946…11491297613153873281

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

7.590 × 10⁹⁷(98-digit number)

75902270169236649893…22982595226307746559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.590 × 10⁹⁷(98-digit number)

75902270169236649893…22982595226307746561

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

1.518 × 10⁹⁸(99-digit number)

15180454033847329978…45965190452615493119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.518 × 10⁹⁸(99-digit number)

15180454033847329978…45965190452615493121

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

3.036 × 10⁹⁸(99-digit number)

30360908067694659957…91930380905230986239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.036 × 10⁹⁸(99-digit number)

30360908067694659957…91930380905230986241

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

6.072 × 10⁹⁸(99-digit number)

60721816135389319915…83860761810461972479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.072 × 10⁹⁸(99-digit number)

60721816135389319915…83860761810461972481

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 #500,606

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