Block #194,968

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/5/2013, 11:39:32 AM · Difficulty 9.8803 · 6,613,932 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

999acfec8c94398726f01850deaceab8b70190cbb067d338c6176152638249c9

View on Chainz ↗

Height

#194,968

Difficulty

9.880315

Transactions

Size

3.90 KB

Version

Bits

09e15c4b

Nonce

1,164,863,769

Timestamp

10/5/2013, 11:39:32 AM

Confirmations

6,613,932

Mined by

⛏️ RO6ANi141hSHQw1CMPWf4B48HG7GAjPkhD1t1

Merkle Root

8e0669546d1cc7736b4bf7ebc90d8885e3669dcdca8cf4ae4ba9e72a65d57564

Transactions (1)

Coinbase8e0669546d1cc7…a9e72a65d57564

1 in → 113 out10.1900 XPM3.81 KB

ANi141hS…jPkhD1t1 AVYzMFMR…wSKWXuy4 Aabufq6z…vs9soDm5 AeSy9sho…wrrT6oQL AGT9hnPx…C3sxd5B5

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.

1.321 × 10⁹³(94-digit number)

13212114130055326434…33064233958772293759

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

1.321 × 10⁹³(94-digit number)

13212114130055326434…33064233958772293759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.321 × 10⁹³(94-digit number)

13212114130055326434…33064233958772293761

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

2.642 × 10⁹³(94-digit number)

26424228260110652868…66128467917544587519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.642 × 10⁹³(94-digit number)

26424228260110652868…66128467917544587521

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

5.284 × 10⁹³(94-digit number)

52848456520221305736…32256935835089175039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.284 × 10⁹³(94-digit number)

52848456520221305736…32256935835089175041

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

1.056 × 10⁹⁴(95-digit number)

10569691304044261147…64513871670178350079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.056 × 10⁹⁴(95-digit number)

10569691304044261147…64513871670178350081

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

2.113 × 10⁹⁴(95-digit number)

21139382608088522294…29027743340356700159

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 #194,968

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