Block #341,263

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/3/2014, 8:35:30 AM · Difficulty 10.1346 · 6,464,734 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3384acafee015cf1956b51c514109e2c76447133be810a80eff229ee93dd57e1

View on Chainz ↗

Height

#341,263

Difficulty

10.134572

Transactions

Size

1.11 KB

Version

Bits

0a227353

Nonce

188,199

Timestamp

1/3/2014, 8:35:30 AM

Confirmations

6,464,734

Mined by

⛏️ 5aRuAQ8QAT3JKsV1xD6zC94z9djnpJrCFKuVbR

Merkle Root

f5797fec8b6909d6fe70b3619c081593d2793631875f0118985725eae296acb3

Transactions (1)

Coinbasef5797fec8b6909…5725eae296acb3

1 in → 29 out9.7000 XPM1.02 KB

AQ8QAT3J…rCFKuVbR AG5YAjec…VhA4Aeh1 ATr7rJvZ…v4W3ybba AeEcKvcg…WKU6G3QF AWCVEa7p…3vPBmiA2

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.

1.624 × 10⁹⁶(97-digit number)

16248127984715042531…39564170323164799999

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

1.624 × 10⁹⁶(97-digit number)

16248127984715042531…39564170323164799999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.624 × 10⁹⁶(97-digit number)

16248127984715042531…39564170323164800001

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

3.249 × 10⁹⁶(97-digit number)

32496255969430085063…79128340646329599999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.249 × 10⁹⁶(97-digit number)

32496255969430085063…79128340646329600001

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

6.499 × 10⁹⁶(97-digit number)

64992511938860170127…58256681292659199999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.499 × 10⁹⁶(97-digit number)

64992511938860170127…58256681292659200001

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

1.299 × 10⁹⁷(98-digit number)

12998502387772034025…16513362585318399999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.299 × 10⁹⁷(98-digit number)

12998502387772034025…16513362585318400001

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

2.599 × 10⁹⁷(98-digit number)

25997004775544068050…33026725170636799999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.599 × 10⁹⁷(98-digit number)

25997004775544068050…33026725170636800001

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