Block #333,998

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/29/2013, 4:46:51 AM · Difficulty 10.1589 · 6,471,867 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1ae5fb6178b0657ec4bdff14863ca650535a274400f2dbdaf3b014ac0be8d955

View on Chainz ↗

Height

#333,998

Difficulty

10.158939

Transactions

Size

2.08 KB

Version

Bits

0a28b03b

Nonce

19,708

Timestamp

12/29/2013, 4:46:51 AM

Confirmations

6,471,867

Mined by

⛏️ P2SHAQo5Sf84DcjUC65gbiaUvY1LDSCktZTnkR

Merkle Root

5246aaf5830986f4decacb1a4a27ffd40436046a85220a5083bbe294c11a15c6

Transactions (3)

Coinbase178a0395fb540f…0f817158b47d6f

1 in → 1 out9.7000 XPM109 B

AQo5Sf84…CktZTnkR

8e32e530f718b2…799a43b7b52dd0

10 in → 2 out10.0284 XPM1.52 KB

AWBo8pdp…hng7sCBq AWby7KFF…zEfUBKDp

ebd4c6d0ef6cfd…e33d557cf5dd44

2 in → 2 out1.9233 XPM374 B

AXofby2w…7Jj7cbAS AQVDx1bg…WkMrQZ9y

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.

7.528 × 10⁹⁹(100-digit number)

75284273554844809428…98972772596903868159

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

7.528 × 10⁹⁹(100-digit number)

75284273554844809428…98972772596903868159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.528 × 10⁹⁹(100-digit number)

75284273554844809428…98972772596903868161

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

1.505 × 10¹⁰⁰(101-digit number)

15056854710968961885…97945545193807736319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.505 × 10¹⁰⁰(101-digit number)

15056854710968961885…97945545193807736321

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

3.011 × 10¹⁰⁰(101-digit number)

30113709421937923771…95891090387615472639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.011 × 10¹⁰⁰(101-digit number)

30113709421937923771…95891090387615472641

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

6.022 × 10¹⁰⁰(101-digit number)

60227418843875847543…91782180775230945279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.022 × 10¹⁰⁰(101-digit number)

60227418843875847543…91782180775230945281

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

1.204 × 10¹⁰¹(102-digit number)

12045483768775169508…83564361550461890559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.204 × 10¹⁰¹(102-digit number)

12045483768775169508…83564361550461890561

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