Block #402,977

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/13/2014, 7:53:40 PM · Difficulty 10.4362 · 6,403,289 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

488b2037be43a9284e4c61bb9222f0d074b8b1dbdfe8f664b03e6566dcef7bcd

View on Chainz ↗

Height

#402,977

Difficulty

10.436173

Transactions

Size

870 B

Version

Bits

0a6fa901

Nonce

112,172

Timestamp

2/13/2014, 7:53:40 PM

Confirmations

6,403,289

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

a804d19906ce92f27bcd6146d17f01c680c56d90bfc249c596af93975ce578a8

Transactions (2)

Coinbasea1c601e9a26c0b…c4486abd15bba9

1 in → 1 out9.1800 XPM110 B

AeKNrjNj…1NEq95Ta

96226fb0afce13…b6532756f26dba

4 in → 2 out7.7855 XPM671 B

AG6iRf2A…MD5gSX4q AYukZDLG…L1spRFjP

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.

5.458 × 10⁹²(93-digit number)

54589166822724889563…01479788975856657279

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

5.458 × 10⁹²(93-digit number)

54589166822724889563…01479788975856657279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.458 × 10⁹²(93-digit number)

54589166822724889563…01479788975856657281

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

1.091 × 10⁹³(94-digit number)

10917833364544977912…02959577951713314559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.091 × 10⁹³(94-digit number)

10917833364544977912…02959577951713314561

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

2.183 × 10⁹³(94-digit number)

21835666729089955825…05919155903426629119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.183 × 10⁹³(94-digit number)

21835666729089955825…05919155903426629121

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

4.367 × 10⁹³(94-digit number)

43671333458179911651…11838311806853258239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.367 × 10⁹³(94-digit number)

43671333458179911651…11838311806853258241

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

8.734 × 10⁹³(94-digit number)

87342666916359823302…23676623613706516479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.734 × 10⁹³(94-digit number)

87342666916359823302…23676623613706516481

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 #402,977

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