Block #565,316

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/28/2014, 6:00:26 AM · Difficulty 10.9650 · 6,261,559 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5c779d159cba821fd40332394cffd9ea79c307036a37e7465d98bb343511056f

View on Chainz ↗

Height

#565,316

Difficulty

10.964988

Transactions

Size

1.33 KB

Version

Bits

0af7097a

Nonce

2,557,448,323

Timestamp

5/28/2014, 6:00:26 AM

Confirmations

6,261,559

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

a5be44c040e10d579317cd7efb7d6e65da92fa1ad7081868c04cb7bec0c59a8f

Transactions (3)

Coinbase892c70e1460409…8db044795a3930

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

f2b9a6b6845ad3…5ea23302809bab

5 in → 1 out200.0000 XPM784 B

ASDVBfFZ…JizKJugo

afdf59f62812d3…c7a88fbf1181ed

2 in → 2 out11.0667 XPM374 B

ALL8Dk3C…85LPVET1 AcXb9hww…EZDriT3f

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.

8.733 × 10⁹⁹(100-digit number)

87339996564598438645…73058916042173501439

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

8.733 × 10⁹⁹(100-digit number)

87339996564598438645…73058916042173501439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.733 × 10⁹⁹(100-digit number)

87339996564598438645…73058916042173501441

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

1.746 × 10¹⁰⁰(101-digit number)

17467999312919687729…46117832084347002879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.746 × 10¹⁰⁰(101-digit number)

17467999312919687729…46117832084347002881

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

3.493 × 10¹⁰⁰(101-digit number)

34935998625839375458…92235664168694005759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.493 × 10¹⁰⁰(101-digit number)

34935998625839375458…92235664168694005761

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

6.987 × 10¹⁰⁰(101-digit number)

69871997251678750916…84471328337388011519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.987 × 10¹⁰⁰(101-digit number)

69871997251678750916…84471328337388011521

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

1.397 × 10¹⁰¹(102-digit number)

13974399450335750183…68942656674776023039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.397 × 10¹⁰¹(102-digit number)

13974399450335750183…68942656674776023041

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 #565,316

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