Block #412,978

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/20/2014, 9:47:31 PM · Difficulty 10.4181 · 6,394,853 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

901049b19887653e74392b00fd31b6119405bac3a91e8d88b633ede4452ba38d

View on Chainz ↗

Height

#412,978

Difficulty

10.418136

Transactions

Size

1.13 KB

Version

Bits

0a6b0af4

Nonce

138,359

Timestamp

2/20/2014, 9:47:31 PM

Confirmations

6,394,853

Mined by

⛏️ 2MaSx,AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

aed05604e05cb9ac40b30a3366c4911be790890820b99d07214e859dc6297e28

Transactions (2)

Coinbasea557b461322097…f82c922c533c5c

1 in → 23 out9.2000 XPM845 B

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

a5811a4d67b4be…02614a6af930f4

1 in → 2 out2.3444 XPM227 B

AMgMQbFw…GMqgtSoB AGSpmj5w…Djj1CLj2

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.

2.590 × 10⁹³(94-digit number)

25905834306116055035…49681928465083177919

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

2.590 × 10⁹³(94-digit number)

25905834306116055035…49681928465083177919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.590 × 10⁹³(94-digit number)

25905834306116055035…49681928465083177921

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

5.181 × 10⁹³(94-digit number)

51811668612232110070…99363856930166355839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.181 × 10⁹³(94-digit number)

51811668612232110070…99363856930166355841

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

1.036 × 10⁹⁴(95-digit number)

10362333722446422014…98727713860332711679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.036 × 10⁹⁴(95-digit number)

10362333722446422014…98727713860332711681

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

2.072 × 10⁹⁴(95-digit number)

20724667444892844028…97455427720665423359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.072 × 10⁹⁴(95-digit number)

20724667444892844028…97455427720665423361

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

4.144 × 10⁹⁴(95-digit number)

41449334889785688056…94910855441330846719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.144 × 10⁹⁴(95-digit number)

41449334889785688056…94910855441330846721

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 #412,978

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