Block #1,524,862

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/3/2016, 6:04:15 PM · Difficulty 10.5992 · 5,292,771 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f218cbf2446522e2f28f9c6a850210e5df38ba1d8f12d7c65ce4e521e8cad85a

View on Chainz ↗

Height

#1,524,862

Difficulty

10.599190

Transactions

Size

1.18 KB

Version

Bits

0a99648a

Nonce

80,421,674

Timestamp

4/3/2016, 6:04:15 PM

Confirmations

5,292,771

Mined by

⛏️ P2SHAeVkNEUaK3v7wtTpz4f9YXiConi3UQFqSs

Merkle Root

1d27c6f2af28a06032cfc2e55b73137351f8f736a6ba7b22dad241d6d5715b27

Transactions (2)

Coinbase70bb63abf5dee2…513924f7f25ca9

1 in → 1 out8.9100 XPM109 B

AeVkNEUa…i3UQFqSs

6d79152cdfbe11…ff506c22b97eb1

1 in → 25 out60.1642 XPM1009 B

AeAH1kct…jLgYaq6x APdrmGpf…yve16r5b ARvfdQDN…ob2aPB2y ARW3axQ3…u1GC9Kds ATqF4pyA…SqVR8YfV

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.

6.096 × 10⁹⁷(98-digit number)

60963412229292262568…08168470096309370879

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

6.096 × 10⁹⁷(98-digit number)

60963412229292262568…08168470096309370879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.096 × 10⁹⁷(98-digit number)

60963412229292262568…08168470096309370881

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

1.219 × 10⁹⁸(99-digit number)

12192682445858452513…16336940192618741759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.219 × 10⁹⁸(99-digit number)

12192682445858452513…16336940192618741761

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

2.438 × 10⁹⁸(99-digit number)

24385364891716905027…32673880385237483519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.438 × 10⁹⁸(99-digit number)

24385364891716905027…32673880385237483521

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

4.877 × 10⁹⁸(99-digit number)

48770729783433810054…65347760770474967039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.877 × 10⁹⁸(99-digit number)

48770729783433810054…65347760770474967041

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

9.754 × 10⁹⁸(99-digit number)

97541459566867620109…30695521540949934079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.754 × 10⁹⁸(99-digit number)

97541459566867620109…30695521540949934081

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 #1,524,862

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