Block #113,518

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/12/2013, 2:22:07 PM · Difficulty 9.7329 · 6,681,700 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3cd6bf0af3d4d43679c378f837f1ccb31bd7451922d3a63f9e62e2981fc25528

View on Chainz ↗

Height

#113,518

Difficulty

9.732936

Transactions

Size

1.29 KB

Version

Bits

09bba1b3

Nonce

21,961

Timestamp

8/12/2013, 2:22:07 PM

Confirmations

6,681,700

Mined by

⛏️ P2SHAHxYTEQEJH1a128ex2ziJsowRTy5namzYw

Merkle Root

bc96b76b18710895e980edd104e1fe0df8c21d7bad4ed698eb89c3dbe64e42a9

Transactions (3)

Coinbaseabb874b6abed8e…2976bf12384d51

1 in → 1 out10.5600 XPM109 B

AHxYTEQE…y5namzYw

5c49fe1be34410…5490c98e149ba8

4 in → 2 out220.0149 XPM667 B

AV3EddNb…vBvMvTaA AMvWpukB…jT76VW35

dd1a15028707d6…dca894e763e6c0

3 in → 2 out50.2926 XPM453 B

AcQ6aJZp…gViFo8mY Ac5JhHyz…hNfncj2a

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.

1.223 × 10⁹⁶(97-digit number)

12239941375009174733…73487583661192528239

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

1.223 × 10⁹⁶(97-digit number)

12239941375009174733…73487583661192528239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.223 × 10⁹⁶(97-digit number)

12239941375009174733…73487583661192528241

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

2.447 × 10⁹⁶(97-digit number)

24479882750018349467…46975167322385056479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.447 × 10⁹⁶(97-digit number)

24479882750018349467…46975167322385056481

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

4.895 × 10⁹⁶(97-digit number)

48959765500036698935…93950334644770112959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.895 × 10⁹⁶(97-digit number)

48959765500036698935…93950334644770112961

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

9.791 × 10⁹⁶(97-digit number)

97919531000073397870…87900669289540225919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.791 × 10⁹⁶(97-digit number)

97919531000073397870…87900669289540225921

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

1.958 × 10⁹⁷(98-digit number)

19583906200014679574…75801338579080451839

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