Block #412,653

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/20/2014, 3:45:46 PM · Difficulty 10.4226 · 6,381,591 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cce67f11028c564003bc45787672a85d19bbeff20746278b743667596b3eff8b

View on Chainz ↗

Height

#412,653

Difficulty

10.422573

Transactions

Size

885 B

Version

Bits

0a6c2dbb

Nonce

825,538

Timestamp

2/20/2014, 3:45:46 PM

Confirmations

6,381,591

Merkle Root

f25740b979c0ddd087c0b1c1dd35c7d6d754018e7730b6d8a9351e0be3d1d035

Transactions (4)

Coinbasecf6bcfc49ada26…0be667531211e3

1 in → 1 out9.2200 XPM116 B

AbwWkWZt…kawDhufa

0356c34c9b8dec…ece38291d0a570

1 in → 2 out6.1127 XPM226 B

AMGKnQ1N…oPijns8W AXNVLKpH…GHdwoAxs

e3e5d50ed7e018…742af52a5a9d90

1 in → 2 out4.0213 XPM225 B

AXnL68UR…jsxeGUhN AHuAaA8D…jzvErjTi

cc29e48f579201…aad25efd949526

1 in → 2 out5.1281 XPM226 B

Acf2a1aq…dA9uiqzp AWNtHyfQ…hXa5dUTH

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.

6.992 × 10⁹⁹(100-digit number)

69928099243584753828…99286949138293002919

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

6.992 × 10⁹⁹(100-digit number)

69928099243584753828…99286949138293002919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.992 × 10⁹⁹(100-digit number)

69928099243584753828…99286949138293002921

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

1.398 × 10¹⁰⁰(101-digit number)

13985619848716950765…98573898276586005839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.398 × 10¹⁰⁰(101-digit number)

13985619848716950765…98573898276586005841

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

2.797 × 10¹⁰⁰(101-digit number)

27971239697433901531…97147796553172011679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.797 × 10¹⁰⁰(101-digit number)

27971239697433901531…97147796553172011681

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

5.594 × 10¹⁰⁰(101-digit number)

55942479394867803062…94295593106344023359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.594 × 10¹⁰⁰(101-digit number)

55942479394867803062…94295593106344023361

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

1.118 × 10¹⁰¹(102-digit number)

11188495878973560612…88591186212688046719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.118 × 10¹⁰¹(102-digit number)

11188495878973560612…88591186212688046721

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