Block #335,323

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/30/2013, 3:34:05 AM · Difficulty 10.1529 · 6,474,529 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a1b46a13dd19a1a36e4dca7ee343c637d0deeceed86f95d27e7d98da69dec700

View on Chainz ↗

Height

#335,323

Difficulty

10.152948

Transactions

Size

655 B

Version

Bits

0a2727a2

Nonce

272,583

Timestamp

12/30/2013, 3:34:05 AM

Confirmations

6,474,529

Mined by

⛏️ P2SHATHeAN619BfQBfVXS5AtuFfTDcVGZ7VquT

Merkle Root

594a67eb9421198f88921251b2b3cee227c2c88334fd2ae7c0ef01030d974b00

Transactions (3)

Coinbase460b115bf8b846…2bf180079eb738

1 in → 1 out9.7100 XPM109 B

ATHeAN61…VGZ7VquT

5f3400ea9c6152…41f8f644500f33

1 in → 2 out9.6300 XPM227 B

AYezLjpH…gDLKM7Vz ASuwkuuz…afoEfUgZ

08c39f521ea0b8…ccb4f201ea6e0e

1 in → 2 out9.6300 XPM226 B

AMisE9oH…ejCxi6Xe AXhH2sBx…No6t6Lp9

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.

3.864 × 10¹⁰¹(102-digit number)

38645187846939069342…34410837049494868479

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

3.864 × 10¹⁰¹(102-digit number)

38645187846939069342…34410837049494868479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.864 × 10¹⁰¹(102-digit number)

38645187846939069342…34410837049494868481

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

7.729 × 10¹⁰¹(102-digit number)

77290375693878138684…68821674098989736959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.729 × 10¹⁰¹(102-digit number)

77290375693878138684…68821674098989736961

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

1.545 × 10¹⁰²(103-digit number)

15458075138775627736…37643348197979473919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.545 × 10¹⁰²(103-digit number)

15458075138775627736…37643348197979473921

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

3.091 × 10¹⁰²(103-digit number)

30916150277551255473…75286696395958947839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.091 × 10¹⁰²(103-digit number)

30916150277551255473…75286696395958947841

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

6.183 × 10¹⁰²(103-digit number)

61832300555102510947…50573392791917895679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.183 × 10¹⁰²(103-digit number)

61832300555102510947…50573392791917895681

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 #335,323

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