Block #341,508

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/3/2014, 12:15:00 PM · Difficulty 10.1385 · 6,464,370 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3c8fc1549762cca368da50023cb4d86f4e97727e8d1decdc96d463cfa5979821

View on Chainz ↗

Height

#341,508

Difficulty

10.138465

Transactions

Size

1.08 KB

Version

Bits

0a23726f

Nonce

44,593

Timestamp

1/3/2014, 12:15:00 PM

Confirmations

6,464,370

Mined by

⛏️ 6aR5AQ8QAT3JKsV1xD6zC94z9djnpJrCFKuVbR

Merkle Root

1002062aa0af2b481c689b8c619742a933034bfbb2c66036f248986c3b75099b

Transactions (1)

Coinbase1002062aa0af2b…48986c3b75099b

1 in → 28 out9.6900 XPM1015 B

AQ8QAT3J…rCFKuVbR AG5YAjec…VhA4Aeh1 AcV2etJ3…AC6C3Zed Adp1wLWz…fELRJLx4 ARkHWBbk…NFGu7Vm7

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.

1.516 × 10⁹⁹(100-digit number)

15166533358619275129…30947141332252029049

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

1.516 × 10⁹⁹(100-digit number)

15166533358619275129…30947141332252029049

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.516 × 10⁹⁹(100-digit number)

15166533358619275129…30947141332252029051

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

3.033 × 10⁹⁹(100-digit number)

30333066717238550259…61894282664504058099

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.033 × 10⁹⁹(100-digit number)

30333066717238550259…61894282664504058101

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

6.066 × 10⁹⁹(100-digit number)

60666133434477100519…23788565329008116199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.066 × 10⁹⁹(100-digit number)

60666133434477100519…23788565329008116201

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

1.213 × 10¹⁰⁰(101-digit number)

12133226686895420103…47577130658016232399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.213 × 10¹⁰⁰(101-digit number)

12133226686895420103…47577130658016232401

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

2.426 × 10¹⁰⁰(101-digit number)

24266453373790840207…95154261316032464799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.426 × 10¹⁰⁰(101-digit number)

24266453373790840207…95154261316032464801

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