Block #342,908

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/4/2014, 9:06:20 AM · Difficulty 10.1639 · 6,450,145 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2961be85e0947035cfa93d1e3ef4d713b35bf6b858e979e4573925ac9496ba4b

View on Chainz ↗

Height

#342,908

Difficulty

10.163934

Transactions

Size

576 B

Version

Bits

0a29f795

Nonce

15,816

Timestamp

1/4/2014, 9:06:20 AM

Confirmations

6,450,145

Merkle Root

6503cf4702e4a816b6d1e044c240e31f07fa3772c88ba6796cc431f3bd993ff1

Transactions (2)

Coinbased4143a21be12f2…0368da6a57d6ff

1 in → 1 out9.6800 XPM109 B

AWT4FajA…7qUxCsaJ

569a252cbb7e8d…fb6dd1ff7cd8a4

2 in → 2 out10.3200 XPM375 B

ANdyMxQd…KmskDavP AX7Gnnzt…ggher9jZ

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.

1.001 × 10¹⁰⁰(101-digit number)

10013005437708340055…94117783997695139599

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

1.001 × 10¹⁰⁰(101-digit number)

10013005437708340055…94117783997695139599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.001 × 10¹⁰⁰(101-digit number)

10013005437708340055…94117783997695139601

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

2.002 × 10¹⁰⁰(101-digit number)

20026010875416680110…88235567995390279199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.002 × 10¹⁰⁰(101-digit number)

20026010875416680110…88235567995390279201

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

4.005 × 10¹⁰⁰(101-digit number)

40052021750833360220…76471135990780558399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.005 × 10¹⁰⁰(101-digit number)

40052021750833360220…76471135990780558401

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

8.010 × 10¹⁰⁰(101-digit number)

80104043501666720440…52942271981561116799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.010 × 10¹⁰⁰(101-digit number)

80104043501666720440…52942271981561116801

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

1.602 × 10¹⁰¹(102-digit number)

16020808700333344088…05884543963122233599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.602 × 10¹⁰¹(102-digit number)

16020808700333344088…05884543963122233601

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