Block #403,241

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/14/2014, 12:53:45 AM · Difficulty 10.4320 · 6,406,046 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1dd0caf2c344e327523cedc43409b9a6cd368a5667a364daae3811d232523cfd

View on Chainz ↗

Height

#403,241

Difficulty

10.431993

Transactions

Size

1003 B

Version

Bits

0a6e9712

Nonce

19,658

Timestamp

2/14/2014, 12:53:45 AM

Confirmations

6,406,046

Mined by

⛏️ 'aRiAGKhfQo2gx6heCfNgerzn5qmLLh7fBXLX6

Merkle Root

1a8e28546927b31ac47aa9639f15a0167d9eff381d6c29d4ea1de49a89af6474

Transactions (1)

Coinbase1a8e28546927b3…1de49a89af6474

1 in → 25 out9.1700 XPM913 B

AGKhfQo2…h7fBXLX6 Aac9Hjdg…P4ktypc3 AYRvXuTr…CkbwFeLY AYtDvcGs…VuAcA7m7 ATKK7iFz…wZm46KN1

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.

2.845 × 10⁹⁵(96-digit number)

28452494219749580293…81237459408431800319

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

2.845 × 10⁹⁵(96-digit number)

28452494219749580293…81237459408431800319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.845 × 10⁹⁵(96-digit number)

28452494219749580293…81237459408431800321

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

5.690 × 10⁹⁵(96-digit number)

56904988439499160587…62474918816863600639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.690 × 10⁹⁵(96-digit number)

56904988439499160587…62474918816863600641

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

1.138 × 10⁹⁶(97-digit number)

11380997687899832117…24949837633727201279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.138 × 10⁹⁶(97-digit number)

11380997687899832117…24949837633727201281

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

2.276 × 10⁹⁶(97-digit number)

22761995375799664235…49899675267454402559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.276 × 10⁹⁶(97-digit number)

22761995375799664235…49899675267454402561

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

4.552 × 10⁹⁶(97-digit number)

45523990751599328470…99799350534908805119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.552 × 10⁹⁶(97-digit number)

45523990751599328470…99799350534908805121

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 #403,241

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