Block #347,765

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/7/2014, 10:04:13 AM · Difficulty 10.2407 · 6,467,121 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d173cbfcfababa4102f56d1981eba665187fb47a268a1677d36e350c5c0965fe

View on Chainz ↗

Height

#347,765

Difficulty

10.240735

Transactions

Size

1.72 KB

Version

Bits

0a3da0d5

Nonce

104,964

Timestamp

1/7/2014, 10:04:13 AM

Confirmations

6,467,121

Mined by

⛏️ uNaR-1AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

a107c63619d20d62e7084864d1b6490ed3744a8275a520e313dee409274c06e7

Transactions (4)

Coinbasea49e3f8b799609…7ca2fafd57437c

1 in → 24 out9.5200 XPM879 B

AQvZBsUo…hppgRZTJ AZV4TwxQ…8JnQqSoH AKzkYQaQ…zR4FspJZ ARSeozDw…C9HtARnj ATKK7iFz…wZm46KN1

ee4b887b96014a…b67f043678d4ed

2 in → 1 out3.0400 XPM342 B

AJ2ew3S7…EHPTaiPf

b2d432e8898c71…819da2926a2462

1 in → 2 out5.5427 XPM225 B

ASanQjQV…2n1F3ZQk AKhr3DRp…QrzBjtBF

7f07d922b0a918…f4cd83f64563e1

1 in → 2 out5.5246 XPM226 B

Aagmg7pp…vTJWmrxm ANx8gQbC…nKpdRXGS

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.

1.252 × 10⁹⁵(96-digit number)

12520837172024488940…77059735864868368959

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

1.252 × 10⁹⁵(96-digit number)

12520837172024488940…77059735864868368959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.252 × 10⁹⁵(96-digit number)

12520837172024488940…77059735864868368961

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

2.504 × 10⁹⁵(96-digit number)

25041674344048977881…54119471729736737919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.504 × 10⁹⁵(96-digit number)

25041674344048977881…54119471729736737921

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

5.008 × 10⁹⁵(96-digit number)

50083348688097955762…08238943459473475839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.008 × 10⁹⁵(96-digit number)

50083348688097955762…08238943459473475841

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

1.001 × 10⁹⁶(97-digit number)

10016669737619591152…16477886918946951679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.001 × 10⁹⁶(97-digit number)

10016669737619591152…16477886918946951681

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

2.003 × 10⁹⁶(97-digit number)

20033339475239182304…32955773837893903359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.003 × 10⁹⁶(97-digit number)

20033339475239182304…32955773837893903361

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 #347,765

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