Block #1,574,105

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/6/2016, 9:25:30 PM · Difficulty 10.7058 · 5,253,063 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1bc8d7aafa118cc5adb99cfae81af18b046f2582447c3d2a715e80d1de4952fc

View on Chainz ↗

Height

#1,574,105

Difficulty

10.705806

Transactions

Size

573 B

Version

Bits

0ab4afac

Nonce

11,245,903

Timestamp

5/6/2016, 9:25:30 PM

Confirmations

5,253,063

Mined by

⛏️ P2SHAcYJH8jFQV8jjcy8ukZwTLLxS9JdXHdRHz

Merkle Root

1f818e8b0afad3a3524053236d32301e200dfbc370e673ede8d19bae913cc9e4

Transactions (2)

Coinbase6b63e8e80b45ea…41e860e5596e55

1 in → 1 out8.7200 XPM110 B

AcYJH8jF…JdXHdRHz

c86352cb5567f9…ab7e929814f6e3

2 in → 2 out0.0278 XPM372 B

AJee3Sbb…xrgzLr9v AeH8Kqc7…6wRcR6Ub

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.

1.031 × 10⁹⁶(97-digit number)

10310111695359132675…70747225389024747519

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

1.031 × 10⁹⁶(97-digit number)

10310111695359132675…70747225389024747519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.031 × 10⁹⁶(97-digit number)

10310111695359132675…70747225389024747521

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

2.062 × 10⁹⁶(97-digit number)

20620223390718265350…41494450778049495039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.062 × 10⁹⁶(97-digit number)

20620223390718265350…41494450778049495041

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

4.124 × 10⁹⁶(97-digit number)

41240446781436530700…82988901556098990079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.124 × 10⁹⁶(97-digit number)

41240446781436530700…82988901556098990081

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

8.248 × 10⁹⁶(97-digit number)

82480893562873061400…65977803112197980159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.248 × 10⁹⁶(97-digit number)

82480893562873061400…65977803112197980161

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

1.649 × 10⁹⁷(98-digit number)

16496178712574612280…31955606224395960319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.649 × 10⁹⁷(98-digit number)

16496178712574612280…31955606224395960321

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 #1,574,105

Cookie Preferences