Block #335,924

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/30/2013, 2:36:57 PM · Difficulty 10.1427 · 6,478,312 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a0c18badd279a7679058ab8baebc866b3173237bc0f7e65cbc9f599bb1e3e275

View on Chainz ↗

Height

#335,924

Difficulty

10.142736

Transactions

Size

879 B

Version

Bits

0a248a54

Nonce

33,581

Timestamp

12/30/2013, 2:36:57 PM

Confirmations

6,478,312

Mined by

⛏️ P2SHAJN1BL9TBJUVXw2rztK9bW4nR6mZU3zTVe

Merkle Root

e825fd8cc1e94df9ee788ea19acb1ce33887353011a55cc68ce784049a8e87aa

Transactions (4)

Coinbase0a45a7b169aed1…a1053bdaae79f0

1 in → 1 out9.7400 XPM109 B

AJN1BL9T…mZU3zTVe

8b3de643eddf9e…d0b13917238ec5

1 in → 4 out9.6500 XPM260 B

ANU8S1BR…65yNoREy AeKNrjNj…1NEq95Ta ALTkzyX5…UeKoYPzu AZJ31Mao…gCve1AhC

ccb389b1f4816f…2752f4a314a47e

1 in → 1 out35.2750 XPM193 B

AMCAMEmf…xHfEV6Gb

b1919b3bbc8976…ccc5ab0d7c41b6

1 in → 2 out3.4437 XPM226 B

ASQdusB2…9e74g5aD AFxmAcfx…c3QXPPHv

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.

1.008 × 10⁹⁸(99-digit number)

10082284728121372571…75745143291788905759

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

1.008 × 10⁹⁸(99-digit number)

10082284728121372571…75745143291788905759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.008 × 10⁹⁸(99-digit number)

10082284728121372571…75745143291788905761

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

2.016 × 10⁹⁸(99-digit number)

20164569456242745143…51490286583577811519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.016 × 10⁹⁸(99-digit number)

20164569456242745143…51490286583577811521

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

4.032 × 10⁹⁸(99-digit number)

40329138912485490287…02980573167155623039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.032 × 10⁹⁸(99-digit number)

40329138912485490287…02980573167155623041

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

8.065 × 10⁹⁸(99-digit number)

80658277824970980575…05961146334311246079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.065 × 10⁹⁸(99-digit number)

80658277824970980575…05961146334311246081

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

1.613 × 10⁹⁹(100-digit number)

16131655564994196115…11922292668622492159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.613 × 10⁹⁹(100-digit number)

16131655564994196115…11922292668622492161

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 #335,924

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