Block #1,574,806

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/7/2016, 11:10:34 AM · Difficulty 10.6984 · 5,252,350 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

20b169369b2d7a706dad01ca6f6befa66eb0d7af85b2e7f9d5a64732fb6a1b2d

View on Chainz ↗

Height

#1,574,806

Difficulty

10.698440

Transactions

Size

971 B

Version

Bits

0ab2ccfb

Nonce

1,944,619,247

Timestamp

5/7/2016, 11:10:34 AM

Confirmations

5,252,350

Mined by

⛏️ P2SHAbwcbX6vTL94d9p2zWcPe1Mcn6fF8b8nfk

Merkle Root

ff125aa1d0ad031dfa0bdd3dfbf890d79f47e96c9a3d6c6bfdbae34a0ab75d47

Transactions (2)

Coinbasea59f05ee4df89e…759c99828e5eb0

1 in → 1 out8.7300 XPM110 B

AbwcbX6v…fF8b8nfk

11e393c62844e2…b28e294812fe2a

1 in → 18 out77.5784 XPM771 B

AW9dmmRi…Nm2s6YtB AYVQ3hHz…Ce6whb4U AemT3Aos…B112cGRK AQ8wzrGp…Fuq2sFPi AQtecpXA…tniescPx

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.

1.269 × 10⁹⁴(95-digit number)

12697832217327214338…49476185683871452159

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

1.269 × 10⁹⁴(95-digit number)

12697832217327214338…49476185683871452159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.269 × 10⁹⁴(95-digit number)

12697832217327214338…49476185683871452161

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

2.539 × 10⁹⁴(95-digit number)

25395664434654428677…98952371367742904319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.539 × 10⁹⁴(95-digit number)

25395664434654428677…98952371367742904321

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

5.079 × 10⁹⁴(95-digit number)

50791328869308857354…97904742735485808639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.079 × 10⁹⁴(95-digit number)

50791328869308857354…97904742735485808641

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

1.015 × 10⁹⁵(96-digit number)

10158265773861771470…95809485470971617279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.015 × 10⁹⁵(96-digit number)

10158265773861771470…95809485470971617281

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

2.031 × 10⁹⁵(96-digit number)

20316531547723542941…91618970941943234559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.031 × 10⁹⁵(96-digit number)

20316531547723542941…91618970941943234561

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 #1,574,806

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