Block #116,911

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/14/2013, 5:21:34 PM · Difficulty 9.7504 · 6,700,526 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9356166ca0578140236bc5b5d62a5feaf53cabb706e2e486fc2b2fdd9983936b

View on Chainz ↗

Height

#116,911

Difficulty

9.750399

Transactions

Size

3.11 KB

Version

Bits

09c01a23

Nonce

114,680

Timestamp

8/14/2013, 5:21:34 PM

Confirmations

6,700,526

Mined by

⛏️ P2SHAP3GRV1JVKTsdnPzeguXK5mjnmXsjhmLZM

Merkle Root

50f864d07cc223695166a93a827ad457b19adff0197877a842af1f46b9fdefe2

Transactions (4)

Coinbasef57a38bad0840e…2e10f662cbd9ea

1 in → 1 out10.5800 XPM109 B

AP3GRV1J…XsjhmLZM

a66b77f53cc0e7…0764013d37a6e7

7 in → 2 out2500.0178 XPM1.09 KB

AJWrQ3s7…7AkNzaXc APVygs7u…KQKb5zxo

c0c46717ff56a8…ad81694183250f

8 in → 1 out1000.0000 XPM1.17 KB

AJWrQ3s7…7AkNzaXc

a57d114c83e054…a2488d30c2341c

4 in → 2 out10.5155 XPM670 B

APYb1S48…jA3jW9C9 AaNMrVuB…vz8xMmHF

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.

5.861 × 10⁹⁷(98-digit number)

58616928843141486806…66168385767514526039

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

5.861 × 10⁹⁷(98-digit number)

58616928843141486806…66168385767514526039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.861 × 10⁹⁷(98-digit number)

58616928843141486806…66168385767514526041

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

1.172 × 10⁹⁸(99-digit number)

11723385768628297361…32336771535029052079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.172 × 10⁹⁸(99-digit number)

11723385768628297361…32336771535029052081

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

2.344 × 10⁹⁸(99-digit number)

23446771537256594722…64673543070058104159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.344 × 10⁹⁸(99-digit number)

23446771537256594722…64673543070058104161

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

4.689 × 10⁹⁸(99-digit number)

46893543074513189444…29347086140116208319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.689 × 10⁹⁸(99-digit number)

46893543074513189444…29347086140116208321

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

9.378 × 10⁹⁸(99-digit number)

93787086149026378889…58694172280232416639

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 #116,911

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