Block #195,912

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/6/2013, 3:32:46 AM · Difficulty 9.8803 · 6,613,970 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4c9b2b8637fc639ad6e9f8f4f709c16462dc3002b2cd825e62fa6c7eae4ab722

View on Chainz ↗

Height

#195,912

Difficulty

9.880323

Transactions

Size

357 B

Version

Bits

09e15ce1

Nonce

129,048

Timestamp

10/6/2013, 3:32:46 AM

Confirmations

6,613,970

Mined by

⛏️ P2SHARqjAnBMQyKVPEuVmLS28AjGE7JJFGsRAX

Merkle Root

29bb21d61759842a411addd74dcd57c9bfd58f43021992f911d261b4a3a5689a

Transactions (2)

Coinbasea7430309b3a94b…e1a320b8079e97

1 in → 1 out10.2400 XPM109 B

ARqjAnBM…JJFGsRAX

09721d688fd9be…89d10c80cb10d8

1 in → 1 out10.2800 XPM158 B

AKVZmjFY…iuD64V6a

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.

5.624 × 10⁹³(94-digit number)

56240556279879708123…25208248628489731519

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

5.624 × 10⁹³(94-digit number)

56240556279879708123…25208248628489731519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.624 × 10⁹³(94-digit number)

56240556279879708123…25208248628489731521

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

1.124 × 10⁹⁴(95-digit number)

11248111255975941624…50416497256979463039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.124 × 10⁹⁴(95-digit number)

11248111255975941624…50416497256979463041

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

2.249 × 10⁹⁴(95-digit number)

22496222511951883249…00832994513958926079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.249 × 10⁹⁴(95-digit number)

22496222511951883249…00832994513958926081

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

4.499 × 10⁹⁴(95-digit number)

44992445023903766498…01665989027917852159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.499 × 10⁹⁴(95-digit number)

44992445023903766498…01665989027917852161

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

8.998 × 10⁹⁴(95-digit number)

89984890047807532997…03331978055835704319

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #195,912

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