Block #1,534,759

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/10/2016, 11:05:52 AM · Difficulty 10.6185 · 5,278,128 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1346befd4f8482d6ef331edbbdc279d9e31d092dc8ad8565ed3bd49b44f1cdef

View on Chainz ↗

Height

#1,534,759

Difficulty

10.618476

Transactions

Size

22.44 KB

Version

Bits

0a9e5476

Nonce

1,543,962,742

Timestamp

4/10/2016, 11:05:52 AM

Confirmations

5,278,128

Mined by

⛏️ P2SHASX4AGyGNDz9pavzMKxfUaB2yZJSgHkikQ

Merkle Root

67752319ca8a30cd62b2704fab83c0767c69971a0476919cd0d68c29d13b39b4

Transactions (4)

Coinbase87a9f069ff78e8…896dde84207df4

1 in → 1 out9.1000 XPM110 B

ASX4AGyG…JSgHkikQ

8edd1df899a88c…07acdc07543f75

51 in → 1 out735.5383 XPM7.41 KB

AaZeiGZn…afdNYgoH

6bb08b3d809787…23dd3401f0aa5a

51 in → 1 out3148.9424 XPM7.41 KB

AVuQvJ3P…QNzcLCji

b86f0ba9ab0f18…7d32d057cde3b5

51 in → 1 out1469.2762 XPM7.42 KB

AUoUdTi8…QVfizkdR

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.

5.081 × 10⁹⁴(95-digit number)

50810412142397274334…32840955262775021879

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

5.081 × 10⁹⁴(95-digit number)

50810412142397274334…32840955262775021879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.081 × 10⁹⁴(95-digit number)

50810412142397274334…32840955262775021881

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

1.016 × 10⁹⁵(96-digit number)

10162082428479454866…65681910525550043759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.016 × 10⁹⁵(96-digit number)

10162082428479454866…65681910525550043761

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

2.032 × 10⁹⁵(96-digit number)

20324164856958909733…31363821051100087519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.032 × 10⁹⁵(96-digit number)

20324164856958909733…31363821051100087521

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

4.064 × 10⁹⁵(96-digit number)

40648329713917819467…62727642102200175039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.064 × 10⁹⁵(96-digit number)

40648329713917819467…62727642102200175041

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

8.129 × 10⁹⁵(96-digit number)

81296659427835638934…25455284204400350079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.129 × 10⁹⁵(96-digit number)

81296659427835638934…25455284204400350081

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 #1,534,759

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