Block #435,026

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/8/2014, 3:32:23 PM · Difficulty 10.3544 · 6,364,506 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9f5c75745710fc86f2cc9426ce1bb3fba883d67a37c9c572ed7b4f66ce651df8

View on Chainz ↗

Height

#435,026

Difficulty

10.354378

Transactions

Size

970 B

Version

Bits

0a5ab88b

Nonce

289,807

Timestamp

3/8/2014, 3:32:23 PM

Confirmations

6,364,506

Mined by

⛏️ RaS7AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

c8068f2b873294059ded9667dbddd0df77a6508598d977d7ad1067c3d5d06ca9

Transactions (1)

Coinbasec8068f2b873294…1067c3d5d06ca9

1 in → 24 out9.3100 XPM879 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGD4yZQw…hGzM2XAx AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

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.

7.557 × 10⁹⁶(97-digit number)

75578875435093712729…13784622674060268219

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

7.557 × 10⁹⁶(97-digit number)

75578875435093712729…13784622674060268219

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.557 × 10⁹⁶(97-digit number)

75578875435093712729…13784622674060268221

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

1.511 × 10⁹⁷(98-digit number)

15115775087018742545…27569245348120536439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.511 × 10⁹⁷(98-digit number)

15115775087018742545…27569245348120536441

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

3.023 × 10⁹⁷(98-digit number)

30231550174037485091…55138490696241072879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.023 × 10⁹⁷(98-digit number)

30231550174037485091…55138490696241072881

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

6.046 × 10⁹⁷(98-digit number)

60463100348074970183…10276981392482145759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.046 × 10⁹⁷(98-digit number)

60463100348074970183…10276981392482145761

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

1.209 × 10⁹⁸(99-digit number)

12092620069614994036…20553962784964291519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.209 × 10⁹⁸(99-digit number)

12092620069614994036…20553962784964291521

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.418 × 10⁹⁸(99-digit number)

24185240139229988073…41107925569928583039

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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