Block #334,043

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/29/2013, 5:34:28 AM · Difficulty 10.1583 · 6,483,124 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

51a9e717041daf79d6e6ab61bb7d0ab9422c0fc1210a9af736d0859628c77272

View on Chainz ↗

Height

#334,043

Difficulty

10.158279

Transactions

Size

1.64 KB

Version

Bits

0a2884f4

Nonce

33,664

Timestamp

12/29/2013, 5:34:28 AM

Confirmations

6,483,124

Mined by

⛏️ aRQfAQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

9aa35a433db1f7da0bdc84047c87b0633d1227dbbd3a9e549d9419501e0732c4

Transactions (4)

Coinbasef41d734f24921e…ac16c90b52ab81

1 in → 25 out9.6800 XPM913 B

AQwRN8bE…V8PsTcY9 Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 Ad9pSzHt…cpJ3y2zz Ae58nAEb…GFUA15fv

144debb7b74519…d90cce4ea49743

1 in → 2 out9.6200 XPM226 B

AXU4oXSJ…TGqt5X5X AU2tCEtW…w5pYH4EP

e4915310537332…743a05513847b1

1 in → 2 out9.6200 XPM226 B

AJUHATMo…t9jkePxK AY9WjN9J…9P2fgksY

e6ec3256a9885d…5fe28979efbe6c

1 in → 2 out8.5069 XPM227 B

AeGkrx8m…V3akuHL7 AMLc22Nd…fkYi7G9J

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.

2.632 × 10⁹⁶(97-digit number)

26324995579251658039…40717620507821721599

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

2.632 × 10⁹⁶(97-digit number)

26324995579251658039…40717620507821721599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.632 × 10⁹⁶(97-digit number)

26324995579251658039…40717620507821721601

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

5.264 × 10⁹⁶(97-digit number)

52649991158503316079…81435241015643443199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.264 × 10⁹⁶(97-digit number)

52649991158503316079…81435241015643443201

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

1.052 × 10⁹⁷(98-digit number)

10529998231700663215…62870482031286886399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.052 × 10⁹⁷(98-digit number)

10529998231700663215…62870482031286886401

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

2.105 × 10⁹⁷(98-digit number)

21059996463401326431…25740964062573772799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.105 × 10⁹⁷(98-digit number)

21059996463401326431…25740964062573772801

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

4.211 × 10⁹⁷(98-digit number)

42119992926802652863…51481928125147545599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.211 × 10⁹⁷(98-digit number)

42119992926802652863…51481928125147545601

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 #334,043

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