Block #394,869

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/8/2014, 6:44:39 AM · Difficulty 10.4196 · 6,401,412 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7602176247c2095fb35f5c4db81920b83a81ccfd598c6b0917b2ca684c53563b

View on Chainz ↗

Height

#394,869

Difficulty

10.419599

Transactions

Size

1.65 KB

Version

Bits

0a6b6adc

Nonce

33,716

Timestamp

2/8/2014, 6:44:39 AM

Confirmations

6,401,412

Mined by

⛏️ uaRZAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

2e5e2fb69103b98c51cc6a66cf32960839517ec31e3c22167a762da1c6eb3f9e

Transactions (2)

Coinbase157441a04dfc26…aabc73dab5e947

1 in → 21 out9.2000 XPM777 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 ALqxX1WA…hsKjbnXn AZV4TwxQ…8JnQqSoH AGKhfQo2…h7fBXLX6

33f1b2bf54c988…93ed6214b5e055

5 in → 2 out279.9284 XPM819 B

AM3Uks4t…pWT7rfZV AWdLxkUp…bXSZYrn9

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.

6.818 × 10⁹⁴(95-digit number)

68187956122519034288…34286759511556908799

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

6.818 × 10⁹⁴(95-digit number)

68187956122519034288…34286759511556908799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.818 × 10⁹⁴(95-digit number)

68187956122519034288…34286759511556908801

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

1.363 × 10⁹⁵(96-digit number)

13637591224503806857…68573519023113817599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.363 × 10⁹⁵(96-digit number)

13637591224503806857…68573519023113817601

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

2.727 × 10⁹⁵(96-digit number)

27275182449007613715…37147038046227635199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.727 × 10⁹⁵(96-digit number)

27275182449007613715…37147038046227635201

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

5.455 × 10⁹⁵(96-digit number)

54550364898015227430…74294076092455270399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.455 × 10⁹⁵(96-digit number)

54550364898015227430…74294076092455270401

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

1.091 × 10⁹⁶(97-digit number)

10910072979603045486…48588152184910540799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.091 × 10⁹⁶(97-digit number)

10910072979603045486…48588152184910540801

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