Block #475,602

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/5/2014, 8:12:28 AM · Difficulty 10.4597 · 6,334,040 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

714fae0578c3a60b4f94358468144b1e066e1784c63ebab42e63beedd7bae7f8

View on Chainz ↗

Height

#475,602

Difficulty

10.459723

Transactions

Size

2.05 KB

Version

Bits

0a75b062

Nonce

55,049

Timestamp

4/5/2014, 8:12:28 AM

Confirmations

6,334,040

Mined by

⛏️ AaS?HAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

76f455d7ba4df0c9ab8ee2900e9d7a73b8c32e4da4fbec8c8bc4668121449869

Transactions (2)

Coinbase4aa4f1a96caed4…69d5da996513d0

1 in → 20 out9.1300 XPM743 B

AQvZBsUo…hppgRZTJ AQ8QAT3J…rCFKuVbR ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn AJtNW28X…Syb4Ph5j

5bb3fb1198c112…6a8fd478c45cc3

8 in → 2 out2.0180 XPM1.23 KB

ATJwK67m…mAF51Xab AdKNUTTc…UrSCafU7

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.

4.291 × 10⁹²(93-digit number)

42917811129674810229…84242249044599060039

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

4.291 × 10⁹²(93-digit number)

42917811129674810229…84242249044599060039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.291 × 10⁹²(93-digit number)

42917811129674810229…84242249044599060041

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

8.583 × 10⁹²(93-digit number)

85835622259349620459…68484498089198120079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.583 × 10⁹²(93-digit number)

85835622259349620459…68484498089198120081

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

1.716 × 10⁹³(94-digit number)

17167124451869924091…36968996178396240159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.716 × 10⁹³(94-digit number)

17167124451869924091…36968996178396240161

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

3.433 × 10⁹³(94-digit number)

34334248903739848183…73937992356792480319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.433 × 10⁹³(94-digit number)

34334248903739848183…73937992356792480321

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

6.866 × 10⁹³(94-digit number)

68668497807479696367…47875984713584960639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.866 × 10⁹³(94-digit number)

68668497807479696367…47875984713584960641

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 #475,602

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