Block #485,311

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/10/2014, 11:55:22 PM · Difficulty 10.6064 · 6,310,412 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

02452e9d207f3290f08e4db84cc35f121bb643932bcdd693d030b97a87b4d711

View on Chainz ↗

Height

#485,311

Difficulty

10.606402

Transactions

Size

649 B

Version

Bits

0a9b3d2d

Nonce

267,776,220

Timestamp

4/10/2014, 11:55:22 PM

Confirmations

6,310,412

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

e5619e364841b9f43e21ae9178c85824ccb086ad62bb94c7f8c87e682111d6f7

Transactions (2)

Coinbasecd866fd3434891…7be761a29f8e99

1 in → 1 out8.8900 XPM116 B

AbwWkWZt…kawDhufa

cc6a1b18230d0e…3151e8671eb2cc

2 in → 6 out18.0300 XPM441 B

ATXFZVYv…JduPzKNb ARoHnwCY…eSXLofWB AcADmAoe…8iNnoMzB AHXJ1dhk…mhL46N6m AcBvLaSu…X3gaHvJ1

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.

1.445 × 10⁹⁹(100-digit number)

14451600754629695480…61623371758830630399

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

1.445 × 10⁹⁹(100-digit number)

14451600754629695480…61623371758830630399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.445 × 10⁹⁹(100-digit number)

14451600754629695480…61623371758830630401

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

2.890 × 10⁹⁹(100-digit number)

28903201509259390960…23246743517661260799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.890 × 10⁹⁹(100-digit number)

28903201509259390960…23246743517661260801

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

5.780 × 10⁹⁹(100-digit number)

57806403018518781920…46493487035322521599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.780 × 10⁹⁹(100-digit number)

57806403018518781920…46493487035322521601

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

1.156 × 10¹⁰⁰(101-digit number)

11561280603703756384…92986974070645043199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.156 × 10¹⁰⁰(101-digit number)

11561280603703756384…92986974070645043201

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

2.312 × 10¹⁰⁰(101-digit number)

23122561207407512768…85973948141290086399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.312 × 10¹⁰⁰(101-digit number)

23122561207407512768…85973948141290086401

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