Block #314,142

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/15/2013, 7:52:46 PM · Difficulty 10.0454 · 6,492,985 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

06b9b6a3ac134a11764129e6eef31b928f960ca250c5724ee00689ae1d69cf07

View on Chainz ↗

Height

#314,142

Difficulty

10.045418

Transactions

Size

1.08 KB

Version

Bits

0a0ba07f

Nonce

52,824

Timestamp

12/15/2013, 7:52:46 PM

Confirmations

6,492,985

Mined by

⛏️ aRAYtDvcGsMH2GY5bD4Hc2rArhMdVuAcA7m7

Merkle Root

3cb528ef2b018833f4fc71d3f7cdc23c56c5aedf61c880f77dfbb88f77b385e0

Transactions (1)

Coinbase3cb528ef2b0188…fbb88f77b385e0

1 in → 28 out9.8700 XPM1015 B

AYtDvcGs…VuAcA7m7 AbtgNzNb…9Atvu81w AQwRN8bE…V8PsTcY9 Aac9Hjdg…P4ktypc3 Ad9pSzHt…cpJ3y2zz

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.

3.490 × 10⁹⁹(100-digit number)

34903251763730736033…84897552723477122279

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

3.490 × 10⁹⁹(100-digit number)

34903251763730736033…84897552723477122279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.490 × 10⁹⁹(100-digit number)

34903251763730736033…84897552723477122281

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

6.980 × 10⁹⁹(100-digit number)

69806503527461472067…69795105446954244559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.980 × 10⁹⁹(100-digit number)

69806503527461472067…69795105446954244561

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

1.396 × 10¹⁰⁰(101-digit number)

13961300705492294413…39590210893908489119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.396 × 10¹⁰⁰(101-digit number)

13961300705492294413…39590210893908489121

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

2.792 × 10¹⁰⁰(101-digit number)

27922601410984588826…79180421787816978239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.792 × 10¹⁰⁰(101-digit number)

27922601410984588826…79180421787816978241

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

5.584 × 10¹⁰⁰(101-digit number)

55845202821969177653…58360843575633956479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.584 × 10¹⁰⁰(101-digit number)

55845202821969177653…58360843575633956481

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 #314,142

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