Block #113,690

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/12/2013, 4:37:26 PM · Difficulty 9.7350 · 6,679,891 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a84b97bce848e493215aaafeed26c43339ce880b6b5f90f40f4e134a0a08932c

View on Chainz ↗

Height

#113,690

Difficulty

9.734955

Transactions

Size

575 B

Version

Bits

09bc2608

Nonce

157,085

Timestamp

8/12/2013, 4:37:26 PM

Confirmations

6,679,891

Merkle Root

ff4d8ce7ad3c7b75497678861f9aa8b03bfdf586e9f15d37b3ca3f518ab42f7c

Transactions (2)

Coinbaseee947eaa18cbdf…2af69f906b5714

1 in → 1 out10.5500 XPM109 B

AVihzcxU…1yT6HvJn

22e6beaf6c7f5a…808733d4edfe17

2 in → 2 out160.0000 XPM375 B

ALkin8fW…T7gcWnes AcWxiJYv…LPH1Kib5

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.

2.099 × 10⁹⁶(97-digit number)

20998104128478139796…18699293182292405479

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

2.099 × 10⁹⁶(97-digit number)

20998104128478139796…18699293182292405479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.099 × 10⁹⁶(97-digit number)

20998104128478139796…18699293182292405481

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

4.199 × 10⁹⁶(97-digit number)

41996208256956279593…37398586364584810959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.199 × 10⁹⁶(97-digit number)

41996208256956279593…37398586364584810961

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

8.399 × 10⁹⁶(97-digit number)

83992416513912559187…74797172729169621919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.399 × 10⁹⁶(97-digit number)

83992416513912559187…74797172729169621921

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

1.679 × 10⁹⁷(98-digit number)

16798483302782511837…49594345458339243839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.679 × 10⁹⁷(98-digit number)

16798483302782511837…49594345458339243841

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

3.359 × 10⁹⁷(98-digit number)

33596966605565023674…99188690916678487679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.359 × 10⁹⁷(98-digit number)

33596966605565023674…99188690916678487681

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