Block #513,206

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/27/2014, 9:14:13 AM · Difficulty 10.8348 · 6,313,938 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

af083434381886fc9a64b50ccf3fef1a781f3b36e5ca90884ed9765c916097de

View on Chainz ↗

Height

#513,206

Difficulty

10.834778

Transactions

Size

834 B

Version

Bits

0ad5b40a

Nonce

52,667

Timestamp

4/27/2014, 9:14:13 AM

Confirmations

6,313,938

Mined by

AREQGaCCeRHuaNkf53p3iT4PbrV47D9Shh

Merkle Root

98288c3741b3e766e0725e89633563fd4e63133230a8df5a390e6ccf561c9243

Transactions (1)

Coinbase98288c3741b3e7…0e6ccf561c9243

1 in → 20 out8.5000 XPM743 B

AREQGaCC…V47D9Shh AGz9gyZW…bo8NYQpw AMVf7Jrg…xd5AVR7C AH5mD99t…Spv1yg4N AbPcCMg4…719q6mAX

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.

6.656 × 10⁹⁶(97-digit number)

66569661741122224278…05235070867445762559

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

6.656 × 10⁹⁶(97-digit number)

66569661741122224278…05235070867445762559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.656 × 10⁹⁶(97-digit number)

66569661741122224278…05235070867445762561

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

1.331 × 10⁹⁷(98-digit number)

13313932348224444855…10470141734891525119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.331 × 10⁹⁷(98-digit number)

13313932348224444855…10470141734891525121

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

2.662 × 10⁹⁷(98-digit number)

26627864696448889711…20940283469783050239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.662 × 10⁹⁷(98-digit number)

26627864696448889711…20940283469783050241

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

5.325 × 10⁹⁷(98-digit number)

53255729392897779422…41880566939566100479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.325 × 10⁹⁷(98-digit number)

53255729392897779422…41880566939566100481

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

1.065 × 10⁹⁸(99-digit number)

10651145878579555884…83761133879132200959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.065 × 10⁹⁸(99-digit number)

10651145878579555884…83761133879132200961

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 #513,206

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