Block #1,534,619

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/10/2016, 8:58:34 AM · Difficulty 10.6173 · 5,289,902 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3ced653c29680a4d29351e43839515dd8ebb96b6349cf82e4eef134fd24024e2

View on Chainz ↗

Height

#1,534,619

Difficulty

10.617277

Transactions

Size

15.02 KB

Version

Bits

0a9e05d8

Nonce

686,518,503

Timestamp

4/10/2016, 8:58:34 AM

Confirmations

5,289,902

Mined by

⛏️ P2SHAHwys6d7xhGrMLitU1WwhYKQRKr2CtHAAW

Merkle Root

01769caa66e447076f437b904229642145ece2dc81df94b7b0ae936df7523c63

Transactions (3)

Coinbasef9d2a0f74072ff…109d59548a0237

1 in → 1 out9.0200 XPM109 B

AHwys6d7…r2CtHAAW

f77519b1669caa…aa5cda6683cdaa

51 in → 1 out1263.2502 XPM7.41 KB

AGoYeZRo…dpzg9CGe

da08d52ef23d6a…35137fe8486c66

51 in → 1 out215.8720 XPM7.42 KB

ALsgHVDY…gKoWyJr9

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.

2.470 × 10⁹⁸(99-digit number)

24707165291232037828…45593266954135142399

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

2.470 × 10⁹⁸(99-digit number)

24707165291232037828…45593266954135142399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.470 × 10⁹⁸(99-digit number)

24707165291232037828…45593266954135142401

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

4.941 × 10⁹⁸(99-digit number)

49414330582464075657…91186533908270284799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.941 × 10⁹⁸(99-digit number)

49414330582464075657…91186533908270284801

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

9.882 × 10⁹⁸(99-digit number)

98828661164928151314…82373067816540569599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.882 × 10⁹⁸(99-digit number)

98828661164928151314…82373067816540569601

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

1.976 × 10⁹⁹(100-digit number)

19765732232985630262…64746135633081139199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.976 × 10⁹⁹(100-digit number)

19765732232985630262…64746135633081139201

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

3.953 × 10⁹⁹(100-digit number)

39531464465971260525…29492271266162278399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.953 × 10⁹⁹(100-digit number)

39531464465971260525…29492271266162278401

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 #1,534,619

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