Block #402,232

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/13/2014, 8:00:03 AM · Difficulty 10.4322 · 6,389,667 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

900e9411507637fb8f03ad6df0d11332c7586d4f2a3c9cc32e5599b569c1ae4c

View on Chainz ↗

Height

#402,232

Difficulty

10.432181

Transactions

Size

367 B

Version

Bits

0a6ea36a

Nonce

159,095

Timestamp

2/13/2014, 8:00:03 AM

Confirmations

6,389,667

Merkle Root

ff95cd4a256f4d6648758f570ac2bd81b1e85422f1d8a127aa341e56891c545d

Transactions (2)

Coinbase34b69f83ec81bd…3ecc58922671e2

1 in → 1 out9.1800 XPM116 B

AbwWkWZt…kawDhufa

3dca5fdf01388a…ffc13901fafbb2

1 in → 1 out9.2300 XPM158 B

AbP1iY2S…QXTtEVYb

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.

2.488 × 10¹⁰¹(102-digit number)

24887877476380971506…18023130215847397599

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

2.488 × 10¹⁰¹(102-digit number)

24887877476380971506…18023130215847397599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.488 × 10¹⁰¹(102-digit number)

24887877476380971506…18023130215847397601

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

4.977 × 10¹⁰¹(102-digit number)

49775754952761943013…36046260431694795199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.977 × 10¹⁰¹(102-digit number)

49775754952761943013…36046260431694795201

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

9.955 × 10¹⁰¹(102-digit number)

99551509905523886027…72092520863389590399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.955 × 10¹⁰¹(102-digit number)

99551509905523886027…72092520863389590401

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

1.991 × 10¹⁰²(103-digit number)

19910301981104777205…44185041726779180799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.991 × 10¹⁰²(103-digit number)

19910301981104777205…44185041726779180801

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

3.982 × 10¹⁰²(103-digit number)

39820603962209554411…88370083453558361599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.982 × 10¹⁰²(103-digit number)

39820603962209554411…88370083453558361601

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