Block #426,652

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/2/2014, 6:57:07 PM · Difficulty 10.3570 · 6,380,072 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c4cdf18c15fcafe98c7ed12e32b493acf5a1b8813154e2ce8dcd3d074ab9b2fe

View on Chainz ↗

Height

#426,652

Difficulty

10.357013

Transactions

Size

1.38 KB

Version

Bits

0a5b6534

Nonce

13,204

Timestamp

3/2/2014, 6:57:07 PM

Confirmations

6,380,072

Mined by

⛏️ P2SHAKCRCCETW8FUumyspNEmHXiVqDqxdRnend

Merkle Root

aec0a347c96c212f55213edb12006cbd0c70c6de81ff094665579962ad926c3a

Transactions (3)

Coinbase0c31504b2b7c3b…2efa44431eb184

1 in → 1 out9.3400 XPM109 B

AKCRCCET…qxdRnend

d59724d4cf8192…364ddf3701c2ab

5 in → 9 out24.6897 XPM988 B

AeKNrjNj…1NEq95Ta AcrH8adE…DfMBAz3M AbwLSonT…FZuaQsbm AV3mC5Sp…WBT3HEs8 AL6hfYqf…jYfKt9LA

4da4642ed1ecb0…a99d3e3c9047f9

1 in → 2 out0.7300 XPM226 B

AX6hy5nv…eKvMAzXW AeAF43gF…Ft72VSyu

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.

3.833 × 10⁹³(94-digit number)

38339640768324382164…92394948955715226719

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

3.833 × 10⁹³(94-digit number)

38339640768324382164…92394948955715226719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.833 × 10⁹³(94-digit number)

38339640768324382164…92394948955715226721

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

7.667 × 10⁹³(94-digit number)

76679281536648764328…84789897911430453439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.667 × 10⁹³(94-digit number)

76679281536648764328…84789897911430453441

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

1.533 × 10⁹⁴(95-digit number)

15335856307329752865…69579795822860906879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.533 × 10⁹⁴(95-digit number)

15335856307329752865…69579795822860906881

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

3.067 × 10⁹⁴(95-digit number)

30671712614659505731…39159591645721813759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.067 × 10⁹⁴(95-digit number)

30671712614659505731…39159591645721813761

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

6.134 × 10⁹⁴(95-digit number)

61343425229319011462…78319183291443627519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.134 × 10⁹⁴(95-digit number)

61343425229319011462…78319183291443627521

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 #426,652

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