Block #1,434,737

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/29/2016, 12:29:23 PM · Difficulty 10.8096 · 5,408,564 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7b74c541909fab6c6cebb8201e9d0adb6e1a9f8ce639082af34b456796e0ef3c

View on Chainz ↗

Height

#1,434,737

Difficulty

10.809596

Transactions

Size

1.36 KB

Version

Bits

0acf41b3

Nonce

388,046,018

Timestamp

1/29/2016, 12:29:23 PM

Confirmations

5,408,564

Mined by

⛏️ P2SHAPmdWjb83JXo2eG5TvWpfv1VK1oyL3BB1a

Merkle Root

68ed83df2415baf45b7af2f3393f1e6df24501dc88ee9c28747e8a3c5691531a

Transactions (3)

Coinbase95424e9e04ebc6…320955d18e91f9

1 in → 1 out8.5600 XPM109 B

APmdWjb8…oyL3BB1a

d02edc71d2c85f…8ab6b4b36f574f

1 in → 2 out448.1700 XPM227 B

ASt3fhyk…kB2zqnKh AHZHhpx8…yMGfDUyH

30b763ebeb7812…4ff9ed29575ebc

6 in → 2 out13.4520 XPM966 B

AULJqW7T…TL2PLdFs AbXdPrQa…Hofg4xBW

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.

3.802 × 10⁹⁵(96-digit number)

38025462304860830662…58968621508436098559

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

3.802 × 10⁹⁵(96-digit number)

38025462304860830662…58968621508436098559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.802 × 10⁹⁵(96-digit number)

38025462304860830662…58968621508436098561

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

7.605 × 10⁹⁵(96-digit number)

76050924609721661325…17937243016872197119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.605 × 10⁹⁵(96-digit number)

76050924609721661325…17937243016872197121

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

1.521 × 10⁹⁶(97-digit number)

15210184921944332265…35874486033744394239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.521 × 10⁹⁶(97-digit number)

15210184921944332265…35874486033744394241

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

3.042 × 10⁹⁶(97-digit number)

30420369843888664530…71748972067488788479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.042 × 10⁹⁶(97-digit number)

30420369843888664530…71748972067488788481

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

6.084 × 10⁹⁶(97-digit number)

60840739687777329060…43497944134977576959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.084 × 10⁹⁶(97-digit number)

60840739687777329060…43497944134977576961

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

1.216 × 10⁹⁷(98-digit number)

12168147937555465812…86995888269955153919

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

Block #1,434,737

Cookie Preferences