Block #395,933

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/9/2014, 2:01:48 AM · Difficulty 10.4098 · 6,430,776 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2029b12e3bed9eb5d6aa3eceb0ff86fc65a6f9ddbe69aaa6c4a7cf9a6ddfa4a6

View on Chainz ↗

Height

#395,933

Difficulty

10.409832

Transactions

Size

1.01 KB

Version

Bits

0a68eac6

Nonce

1,476,748

Timestamp

2/9/2014, 2:01:48 AM

Confirmations

6,430,776

Mined by

⛏️ aRAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

438a12cc79626697c445db47aa6e9bfbf0a5cca32dd236da05a025f7d4d88bf8

Transactions (1)

Coinbase438a12cc796266…a025f7d4d88bf8

1 in → 26 out9.2100 XPM947 B

Aac9Hjdg…P4ktypc3 ALqxX1WA…hsKjbnXn AGKhfQo2…h7fBXLX6 AZV4TwxQ…8JnQqSoH Af76ewER…EzGhbQ6S

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.

6.627 × 10⁹⁸(99-digit number)

66278466936372955224…17072190865820430239

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

6.627 × 10⁹⁸(99-digit number)

66278466936372955224…17072190865820430239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.627 × 10⁹⁸(99-digit number)

66278466936372955224…17072190865820430241

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

1.325 × 10⁹⁹(100-digit number)

13255693387274591044…34144381731640860479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.325 × 10⁹⁹(100-digit number)

13255693387274591044…34144381731640860481

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

2.651 × 10⁹⁹(100-digit number)

26511386774549182089…68288763463281720959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.651 × 10⁹⁹(100-digit number)

26511386774549182089…68288763463281720961

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

5.302 × 10⁹⁹(100-digit number)

53022773549098364179…36577526926563441919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.302 × 10⁹⁹(100-digit number)

53022773549098364179…36577526926563441921

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

1.060 × 10¹⁰⁰(101-digit number)

10604554709819672835…73155053853126883839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.060 × 10¹⁰⁰(101-digit number)

10604554709819672835…73155053853126883841

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 #395,933

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