Block #357,873

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/13/2014, 4:41:24 PM · Difficulty 10.3894 · 6,450,248 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b6e038baad37518e8a1f71b2cc46abc8fd60a1c908f95b16f87fed89de7411ee

View on Chainz ↗

Height

#357,873

Difficulty

10.389397

Transactions

Size

1.01 KB

Version

Bits

0a63af84

Nonce

1,447

Timestamp

1/13/2014, 4:41:24 PM

Confirmations

6,450,248

Mined by

⛏️ uaRAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

a29cefc80697ac6423f172e5e16eeea1f188048fbadbcfd6f0ec52a46a4e9849

Transactions (1)

Coinbasea29cefc80697ac…ec52a46a4e9849

1 in → 26 out9.2500 XPM947 B

Aac9Hjdg…P4ktypc3 ANeHTs9o…oazVAG8Z APXXNbFp…SppKjmSN AQ8QAT3J…rCFKuVbR ARSeozDw…C9HtARnj

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.

8.033 × 10⁹²(93-digit number)

80336963214419484468…37853815594407812159

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

8.033 × 10⁹²(93-digit number)

80336963214419484468…37853815594407812159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.033 × 10⁹²(93-digit number)

80336963214419484468…37853815594407812161

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

1.606 × 10⁹³(94-digit number)

16067392642883896893…75707631188815624319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.606 × 10⁹³(94-digit number)

16067392642883896893…75707631188815624321

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

3.213 × 10⁹³(94-digit number)

32134785285767793787…51415262377631248639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.213 × 10⁹³(94-digit number)

32134785285767793787…51415262377631248641

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

6.426 × 10⁹³(94-digit number)

64269570571535587574…02830524755262497279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.426 × 10⁹³(94-digit number)

64269570571535587574…02830524755262497281

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

1.285 × 10⁹⁴(95-digit number)

12853914114307117514…05661049510524994559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.285 × 10⁹⁴(95-digit number)

12853914114307117514…05661049510524994561

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 #357,873

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