Block #1,534,715

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/10/2016, 10:27:18 AM · Difficulty 10.6180 · 5,274,467 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1b236b54fd8519ecc9239426bb6c514ab6d27b55d4b25a6c303169387a289bda

View on Chainz ↗

Height

#1,534,715

Difficulty

10.617978

Transactions

Size

7.60 KB

Version

Bits

0a9e33d4

Nonce

1,764,844,760

Timestamp

4/10/2016, 10:27:18 AM

Confirmations

5,274,467

Mined by

⛏️ P2SHARdYqobAR7DT9Uukwiu3Zzx8KnCQv9PowN

Merkle Root

6091b380c71b55c8f2862239162b9dfd44c84fc9ec81dc46661d46a716b0e59c

Transactions (2)

Coinbasea04e2599e1286e…939366a3c0b7c9

1 in → 1 out8.9400 XPM109 B

ARdYqobA…CQv9PowN

325c03f44a29bb…22da9f9ac24d18

51 in → 1 out3089.0889 XPM7.41 KB

ARfSmwrX…KZwJ4Tx2

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.

1.396 × 10⁹⁸(99-digit number)

13969251159936670573…09868384525793443839

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

1.396 × 10⁹⁸(99-digit number)

13969251159936670573…09868384525793443839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.396 × 10⁹⁸(99-digit number)

13969251159936670573…09868384525793443841

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

2.793 × 10⁹⁸(99-digit number)

27938502319873341146…19736769051586887679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.793 × 10⁹⁸(99-digit number)

27938502319873341146…19736769051586887681

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

5.587 × 10⁹⁸(99-digit number)

55877004639746682292…39473538103173775359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.587 × 10⁹⁸(99-digit number)

55877004639746682292…39473538103173775361

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

1.117 × 10⁹⁹(100-digit number)

11175400927949336458…78947076206347550719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.117 × 10⁹⁹(100-digit number)

11175400927949336458…78947076206347550721

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

2.235 × 10⁹⁹(100-digit number)

22350801855898672917…57894152412695101439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.235 × 10⁹⁹(100-digit number)

22350801855898672917…57894152412695101441

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

4.470 × 10⁹⁹(100-digit number)

44701603711797345834…15788304825390202879

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 #1,534,715

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