Block #1,534,524

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/10/2016, 7:27:35 AM · Difficulty 10.6170 · 5,283,002 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4aeb96ef488d2a7648c0ad5fd8f09066360e833ae9304771daa289ce50d71734

View on Chainz ↗

Height

#1,534,524

Difficulty

10.617007

Transactions

Size

8.25 KB

Version

Bits

0a9df424

Nonce

860,674,149

Timestamp

4/10/2016, 7:27:35 AM

Confirmations

5,283,002

Mined by

⛏️ P2SHAMoqiJJ3VWpTMrghBZmSGcuY6Gq7YwJ9Qv

Merkle Root

bf364a578976d770691f9d44ed2d77be71e087277f3d5138a70e8cc67212d44c

Transactions (3)

Coinbasec357034b473ef1…ffd2c42bd54c00

1 in → 1 out8.9500 XPM109 B

AMoqiJJ3…q7YwJ9Qv

6da4f44a4dc822…aae058acd7bf72

4 in → 2 out184.5000 XPM670 B

AVbJyRrt…ckKmruYL AJVeRHXf…C2yREH1f

67e219297dfef8…f4af11d2c16b01

51 in → 1 out1151.5625 XPM7.41 KB

AQodQKeB…y38VSzzB

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.

3.541 × 10⁹⁵(96-digit number)

35410542081613488249…49550755045117457279

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

3.541 × 10⁹⁵(96-digit number)

35410542081613488249…49550755045117457279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.541 × 10⁹⁵(96-digit number)

35410542081613488249…49550755045117457281

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

7.082 × 10⁹⁵(96-digit number)

70821084163226976499…99101510090234914559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.082 × 10⁹⁵(96-digit number)

70821084163226976499…99101510090234914561

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

1.416 × 10⁹⁶(97-digit number)

14164216832645395299…98203020180469829119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.416 × 10⁹⁶(97-digit number)

14164216832645395299…98203020180469829121

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

2.832 × 10⁹⁶(97-digit number)

28328433665290790599…96406040360939658239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.832 × 10⁹⁶(97-digit number)

28328433665290790599…96406040360939658241

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

5.665 × 10⁹⁶(97-digit number)

56656867330581581199…92812080721879316479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.665 × 10⁹⁶(97-digit number)

56656867330581581199…92812080721879316481

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 #1,534,524

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