Block #403,914

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/14/2014, 12:04:20 PM · Difficulty 10.4324 · 6,402,336 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

41bddab4e9dd03f1ddabf3f05b0fc72ab1f4f60e6d3d46928b4f32034690c55f

View on Chainz ↗

Height

#403,914

Difficulty

10.432387

Transactions

Size

867 B

Version

Bits

0a6eb0eb

Nonce

1,602

Timestamp

2/14/2014, 12:04:20 PM

Confirmations

6,402,336

Mined by

⛏️ aR?yAYRvXuTr13MD4FS87pKR469j8hCkbwFeLY

Merkle Root

52cb74b3c87f814d9b658ec2759a73577626bd2f27b37890355af528086efd1f

Transactions (1)

Coinbase52cb74b3c87f81…5af528086efd1f

1 in → 21 out9.1700 XPM777 B

AYRvXuTr…CkbwFeLY AQvZBsUo…hppgRZTJ Af76ewER…EzGhbQ6S AZV4TwxQ…8JnQqSoH AGKhfQo2…h7fBXLX6

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.

1.504 × 10⁹⁵(96-digit number)

15046858097670819807…37895809204324236479

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

1.504 × 10⁹⁵(96-digit number)

15046858097670819807…37895809204324236479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.504 × 10⁹⁵(96-digit number)

15046858097670819807…37895809204324236481

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

3.009 × 10⁹⁵(96-digit number)

30093716195341639614…75791618408648472959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.009 × 10⁹⁵(96-digit number)

30093716195341639614…75791618408648472961

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

6.018 × 10⁹⁵(96-digit number)

60187432390683279228…51583236817296945919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.018 × 10⁹⁵(96-digit number)

60187432390683279228…51583236817296945921

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

1.203 × 10⁹⁶(97-digit number)

12037486478136655845…03166473634593891839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.203 × 10⁹⁶(97-digit number)

12037486478136655845…03166473634593891841

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

2.407 × 10⁹⁶(97-digit number)

24074972956273311691…06332947269187783679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.407 × 10⁹⁶(97-digit number)

24074972956273311691…06332947269187783681

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 #403,914

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