Block #346,988

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/6/2014, 9:31:17 PM · Difficulty 10.2371 · 6,463,863 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a6cc358132052ca3e70dbee2609082c7ed7c2f7a2e882b01c9e2243fe66d6060

View on Chainz ↗

Height

#346,988

Difficulty

10.237058

Transactions

Size

1.11 KB

Version

Bits

0a3cafce

Nonce

58,705

Timestamp

1/6/2014, 9:31:17 PM

Confirmations

6,463,863

Mined by

⛏️ P2SHAXJ7s9EfbGd5iVqwksTT5GJH6DaerLwin1

Merkle Root

247827bbcc710772a8faa10ff1588b837162cf714a1c5a058e451613ad0636e6

Transactions (4)

Coinbase4aad0923a3376c…54123acb6cf321

1 in → 1 out9.5600 XPM109 B

AXJ7s9Ef…aerLwin1

6f7d9d0bf78c25…866e2a5ed813ab

3 in → 1 out2.4800 XPM487 B

AcF528jR…THtDdS57

c82fd64503e8fe…be9eb90a75d8ef

1 in → 2 out6.5398 XPM225 B

AQnWMim4…qG8rjHWB AdDAwTBa…WdqY6Phs

04c2c99fed3335…bb6c9b76035d89

1 in → 2 out2.5545 XPM227 B

AWKMGspb…cs45d2ci AYNogAbj…4nBABbo8

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.

2.595 × 10⁹⁷(98-digit number)

25952441331660446915…05386657763517649479

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

2.595 × 10⁹⁷(98-digit number)

25952441331660446915…05386657763517649479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.595 × 10⁹⁷(98-digit number)

25952441331660446915…05386657763517649481

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

5.190 × 10⁹⁷(98-digit number)

51904882663320893830…10773315527035298959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.190 × 10⁹⁷(98-digit number)

51904882663320893830…10773315527035298961

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

1.038 × 10⁹⁸(99-digit number)

10380976532664178766…21546631054070597919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.038 × 10⁹⁸(99-digit number)

10380976532664178766…21546631054070597921

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

2.076 × 10⁹⁸(99-digit number)

20761953065328357532…43093262108141195839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.076 × 10⁹⁸(99-digit number)

20761953065328357532…43093262108141195841

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

4.152 × 10⁹⁸(99-digit number)

41523906130656715064…86186524216282391679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.152 × 10⁹⁸(99-digit number)

41523906130656715064…86186524216282391681

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 #346,988

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