Block #427,200

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/3/2014, 5:35:47 AM · Difficulty 10.3459 · 6,404,386 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2290cd479412774f08bdd3b1f8423b0d0cfa6ee2d42b5d2b082f49c668631d7e

View on Chainz ↗

Height

#427,200

Difficulty

10.345908

Transactions

Size

1.14 KB

Version

Bits

0a588d6a

Nonce

60,947

Timestamp

3/3/2014, 5:35:47 AM

Confirmations

6,404,386

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

01f9c2f7ef7ce38b1685d3dd6140a9cb5876d3e6e49b5c7e9b276dc8b358eef9

Transactions (2)

Coinbase7165d87e7265d4…3f8e167cd02757

1 in → 1 out9.3400 XPM110 B

AeKNrjNj…1NEq95Ta

ccbf99c4d40082…58223d09483390

6 in → 2 out6000.5250 XPM961 B

AesXDGcs…kUFyxJcZ AWVYyEgA…aNV9frmu

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.

1.224 × 10¹⁰²(103-digit number)

12243963970353046486…03952180144423413759

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

1.224 × 10¹⁰²(103-digit number)

12243963970353046486…03952180144423413759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.224 × 10¹⁰²(103-digit number)

12243963970353046486…03952180144423413761

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

2.448 × 10¹⁰²(103-digit number)

24487927940706092973…07904360288846827519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.448 × 10¹⁰²(103-digit number)

24487927940706092973…07904360288846827521

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

4.897 × 10¹⁰²(103-digit number)

48975855881412185947…15808720577693655039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.897 × 10¹⁰²(103-digit number)

48975855881412185947…15808720577693655041

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

9.795 × 10¹⁰²(103-digit number)

97951711762824371894…31617441155387310079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.795 × 10¹⁰²(103-digit number)

97951711762824371894…31617441155387310081

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

1.959 × 10¹⁰³(104-digit number)

19590342352564874378…63234882310774620159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.959 × 10¹⁰³(104-digit number)

19590342352564874378…63234882310774620161

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 #427,200

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