Block #564,739

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/27/2014, 9:04:07 PM · Difficulty 10.9647 · 6,251,316 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1ccff313b378b8078060ab032923df874475af53717a7fef9545f6ab78ae47b3

View on Chainz ↗

Height

#564,739

Difficulty

10.964676

Transactions

Size

923 B

Version

Bits

0af6f509

Nonce

759,801,980

Timestamp

5/27/2014, 9:04:07 PM

Confirmations

6,251,316

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

9b941dc13e65ad2730a6203bdfde581f670e0bbb1ef01762b8bfd9affd339aa9

Transactions (3)

Coinbasef88f59e1f89d3b…9dd3c40ebb7f97

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

07d86aee43bea7…e867cf336d3355

3 in → 1 out41.8477 XPM488 B

AbFVRscN…qpN5k491

1a679a749af001…1740da04c9297b

1 in → 2 out3.9854 XPM227 B

AMY1NkuG…ZJxBzH6H AZknZb9b…bVU5VHFw

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.

1.877 × 10⁹⁹(100-digit number)

18775302756021819955…58225553904237189119

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

1.877 × 10⁹⁹(100-digit number)

18775302756021819955…58225553904237189119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.877 × 10⁹⁹(100-digit number)

18775302756021819955…58225553904237189121

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

3.755 × 10⁹⁹(100-digit number)

37550605512043639911…16451107808474378239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.755 × 10⁹⁹(100-digit number)

37550605512043639911…16451107808474378241

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

7.510 × 10⁹⁹(100-digit number)

75101211024087279822…32902215616948756479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.510 × 10⁹⁹(100-digit number)

75101211024087279822…32902215616948756481

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

1.502 × 10¹⁰⁰(101-digit number)

15020242204817455964…65804431233897512959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.502 × 10¹⁰⁰(101-digit number)

15020242204817455964…65804431233897512961

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

3.004 × 10¹⁰⁰(101-digit number)

30040484409634911929…31608862467795025919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.004 × 10¹⁰⁰(101-digit number)

30040484409634911929…31608862467795025921

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 #564,739

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