Block #565,522

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/28/2014, 8:51:44 AM · Difficulty 10.9652 · 6,251,162 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d5203c59108eea10586ab41a9971904afdff91d7547588d196c18960c0079376

View on Chainz ↗

Height

#565,522

Difficulty

10.965224

Transactions

Size

1.15 KB

Version

Bits

0af718f3

Nonce

10,066,876

Timestamp

5/28/2014, 8:51:44 AM

Confirmations

6,251,162

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

bd07cf77181201eeb302d50fac90bc0f9124e2b47464fbf31cc072407407b819

Transactions (4)

Coinbase38723bbcc740fd…3a2714265daf49

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

4d27287c1b5fc6…3fa62c68a98512

3 in → 2 out4000.0100 XPM522 B

ATviY9cD…uJLk6eu3 AFtwRAEY…gp4etVu7

e6dcc4aa3a1fe7…6ba296201098ce

1 in → 2 out8.2900 XPM226 B

APqGncrk…wU2oaa8x AVQ5uZUo…s7JZA7HP

06b10d4c727b0b…5120866d646114

1 in → 2 out3.2249 XPM226 B

AHwzn16H…wQPtXoSA AS9ZCvju…bu3NEFwZ

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.

2.745 × 10¹⁰⁰(101-digit number)

27454168753305491698…31263334557042570239

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

2.745 × 10¹⁰⁰(101-digit number)

27454168753305491698…31263334557042570239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.745 × 10¹⁰⁰(101-digit number)

27454168753305491698…31263334557042570241

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

5.490 × 10¹⁰⁰(101-digit number)

54908337506610983396…62526669114085140479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.490 × 10¹⁰⁰(101-digit number)

54908337506610983396…62526669114085140481

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

1.098 × 10¹⁰¹(102-digit number)

10981667501322196679…25053338228170280959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.098 × 10¹⁰¹(102-digit number)

10981667501322196679…25053338228170280961

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

2.196 × 10¹⁰¹(102-digit number)

21963335002644393358…50106676456340561919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.196 × 10¹⁰¹(102-digit number)

21963335002644393358…50106676456340561921

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

4.392 × 10¹⁰¹(102-digit number)

43926670005288786717…00213352912681123839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.392 × 10¹⁰¹(102-digit number)

43926670005288786717…00213352912681123841

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

8.785 × 10¹⁰¹(102-digit number)

87853340010577573434…00426705825362247679

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #565,522

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