Block #417,459

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/24/2014, 4:43:21 AM · Difficulty 10.3906 · 6,389,248 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fddeb4ea0a51b36c0ae99fb69e80cec9aafcf068734e4a3c0566e6b38c8a1469

View on Chainz ↗

Height

#417,459

Difficulty

10.390556

Transactions

Size

867 B

Version

Bits

0a63fb7f

Nonce

324,484

Timestamp

2/24/2014, 4:43:21 AM

Confirmations

6,389,248

Mined by

⛏️ ^aSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

dba55850e080f1a3e2320140fe158d7ffcdb3800c5129fa7fc6a71f0cbe73ad6

Transactions (1)

Coinbasedba55850e080f1…6a71f0cbe73ad6

1 in → 21 out9.2500 XPM777 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AZV4TwxQ…8JnQqSoH AGKhfQo2…h7fBXLX6 AJLB8H7s…MRD4s5wA

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.

1.176 × 10⁹⁴(95-digit number)

11761774292070260578…32128007153593464639

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

1.176 × 10⁹⁴(95-digit number)

11761774292070260578…32128007153593464639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.176 × 10⁹⁴(95-digit number)

11761774292070260578…32128007153593464641

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

2.352 × 10⁹⁴(95-digit number)

23523548584140521157…64256014307186929279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.352 × 10⁹⁴(95-digit number)

23523548584140521157…64256014307186929281

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

4.704 × 10⁹⁴(95-digit number)

47047097168281042315…28512028614373858559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.704 × 10⁹⁴(95-digit number)

47047097168281042315…28512028614373858561

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

9.409 × 10⁹⁴(95-digit number)

94094194336562084630…57024057228747717119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.409 × 10⁹⁴(95-digit number)

94094194336562084630…57024057228747717121

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

1.881 × 10⁹⁵(96-digit number)

18818838867312416926…14048114457495434239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.881 × 10⁹⁵(96-digit number)

18818838867312416926…14048114457495434241

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 #417,459

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