Block #1,564,773

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/29/2016, 8:05:21 PM · Difficulty 10.7500 · 5,262,463 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5b8e67f82bd9f59d135fa67b60bada26ed72c7780990faffec59bb0b7f987833

View on Chainz ↗

Height

#1,564,773

Difficulty

10.750011

Transactions

Size

1.28 KB

Version

Bits

0ac000b9

Nonce

1,371,172,862

Timestamp

4/29/2016, 8:05:21 PM

Confirmations

5,262,463

Mined by

⛏️ P2SHAbzsiQrwfathf35QK7Z9qXQjqpiBu598Px

Merkle Root

6615dbe7601992569de6c71300b5590905e9285f9f810d32199b7f3000e916b6

Transactions (2)

Coinbase7f6fee7f97c058…221b85da2b019e

1 in → 1 out8.6600 XPM109 B

AbzsiQrw…iBu598Px

708cc2a59fdd9a…b73000a782ec88

1 in → 28 out216.2374 XPM1.08 KB

AWn3KdL9…mu2nFoor APuxoYC6…aSKJDCEB Aejy7AaU…d2cWkHZD AbvTDP5X…QiZ6LJeB ATZ9JsHQ…vbcmrGNk

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.

5.818 × 10⁹⁶(97-digit number)

58181820918693666651…23639242979881492479

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

5.818 × 10⁹⁶(97-digit number)

58181820918693666651…23639242979881492479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.818 × 10⁹⁶(97-digit number)

58181820918693666651…23639242979881492481

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

1.163 × 10⁹⁷(98-digit number)

11636364183738733330…47278485959762984959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.163 × 10⁹⁷(98-digit number)

11636364183738733330…47278485959762984961

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

2.327 × 10⁹⁷(98-digit number)

23272728367477466660…94556971919525969919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.327 × 10⁹⁷(98-digit number)

23272728367477466660…94556971919525969921

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

4.654 × 10⁹⁷(98-digit number)

46545456734954933321…89113943839051939839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.654 × 10⁹⁷(98-digit number)

46545456734954933321…89113943839051939841

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

9.309 × 10⁹⁷(98-digit number)

93090913469909866642…78227887678103879679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.309 × 10⁹⁷(98-digit number)

93090913469909866642…78227887678103879681

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 #1,564,773

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