Block #346,799

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/6/2014, 6:44:01 PM · Difficulty 10.2337 · 6,461,210 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

94a7c8c65ebbf264acde690e6fb0aaaef3634bb8bf7093273120abf1b5c0f364

View on Chainz ↗

Height

#346,799

Difficulty

10.233722

Transactions

Size

1.01 KB

Version

Bits

0a3bd537

Nonce

18,971

Timestamp

1/6/2014, 6:44:01 PM

Confirmations

6,461,210

Mined by

⛏️ JaRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

dde41aa5b63a2282ac601cab38daee44913ae1aa859a5f860aff6eaa79b3025d

Transactions (1)

Coinbasedde41aa5b63a22…ff6eaa79b3025d

1 in → 26 out9.5300 XPM947 B

AQvZBsUo…hppgRZTJ AQwRN8bE…V8PsTcY9 AJzWx2VD…j4ZSMit5 Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7

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.

7.332 × 10⁸⁹(90-digit number)

73323954888255506863…33223256607359854079

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

7.332 × 10⁸⁹(90-digit number)

73323954888255506863…33223256607359854079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.332 × 10⁸⁹(90-digit number)

73323954888255506863…33223256607359854081

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

1.466 × 10⁹⁰(91-digit number)

14664790977651101372…66446513214719708159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.466 × 10⁹⁰(91-digit number)

14664790977651101372…66446513214719708161

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

2.932 × 10⁹⁰(91-digit number)

29329581955302202745…32893026429439416319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.932 × 10⁹⁰(91-digit number)

29329581955302202745…32893026429439416321

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

5.865 × 10⁹⁰(91-digit number)

58659163910604405490…65786052858878832639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.865 × 10⁹⁰(91-digit number)

58659163910604405490…65786052858878832641

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

1.173 × 10⁹¹(92-digit number)

11731832782120881098…31572105717757665279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.173 × 10⁹¹(92-digit number)

11731832782120881098…31572105717757665281

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 #346,799

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