Block #338,490

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/1/2014, 11:25:43 AM · Difficulty 10.1221 · 6,475,637 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f2d3e5efdea530d09510b7754d0c3862ecff6c1ae18fe4cac382b203f5fa902f

View on Chainz ↗

Height

#338,490

Difficulty

10.122105

Transactions

Size

1.08 KB

Version

Bits

0a1f4247

Nonce

235,628

Timestamp

1/1/2014, 11:25:43 AM

Confirmations

6,475,637

Mined by

⛏️ :*aRAPeshfYVKJ2qg4aRhC5FMjPmxg3PKcKMKH

Merkle Root

9a8f3f2ce9c0a1e7313b591ed57244220188f310582b3ec3a9b31d82910b70c7

Transactions (1)

Coinbase9a8f3f2ce9c0a1…b31d82910b70c7

1 in → 28 out9.7300 XPM1015 B

APeshfYV…3PKcKMKH AQ8QAT3J…rCFKuVbR Aac9Hjdg…P4ktypc3 AG5YAjec…VhA4Aeh1 AJzWx2VD…j4ZSMit5

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.

2.470 × 10⁹⁹(100-digit number)

24703834836867987750…31022948936530175999

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

2.470 × 10⁹⁹(100-digit number)

24703834836867987750…31022948936530175999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.470 × 10⁹⁹(100-digit number)

24703834836867987750…31022948936530176001

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

4.940 × 10⁹⁹(100-digit number)

49407669673735975500…62045897873060351999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.940 × 10⁹⁹(100-digit number)

49407669673735975500…62045897873060352001

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

9.881 × 10⁹⁹(100-digit number)

98815339347471951000…24091795746120703999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.881 × 10⁹⁹(100-digit number)

98815339347471951000…24091795746120704001

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

1.976 × 10¹⁰⁰(101-digit number)

19763067869494390200…48183591492241407999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.976 × 10¹⁰⁰(101-digit number)

19763067869494390200…48183591492241408001

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

3.952 × 10¹⁰⁰(101-digit number)

39526135738988780400…96367182984482815999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.952 × 10¹⁰⁰(101-digit number)

39526135738988780400…96367182984482816001

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 #338,490

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