Block #113,469

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/12/2013, 1:41:46 PM · Difficulty 9.7325 · 6,694,418 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

317919795f49d9f2dd637dec020343cda1f4c752743dde63baab0fc7afd160f7

View on Chainz ↗

Height

#113,469

Difficulty

9.732516

Transactions

Size

200 B

Version

Bits

09bb8624

Nonce

505,519

Timestamp

8/12/2013, 1:41:46 PM

Confirmations

6,694,418

Mined by

⛏️ P2SHAaLrWjpuCAcVSwh3UXs9hmrdJsQmdcRbaT

Merkle Root

c3ac3601dc62b340984d5b7181ee8360ef4e08276ac0310d9063879cb3760115

Transactions (1)

Coinbasec3ac3601dc62b3…63879cb3760115

1 in → 1 out10.5400 XPM109 B

AaLrWjpu…QmdcRbaT

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.

2.302 × 10⁹⁸(99-digit number)

23023184603348537758…91004650484522987519

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

2.302 × 10⁹⁸(99-digit number)

23023184603348537758…91004650484522987519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.302 × 10⁹⁸(99-digit number)

23023184603348537758…91004650484522987521

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

4.604 × 10⁹⁸(99-digit number)

46046369206697075516…82009300969045975039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.604 × 10⁹⁸(99-digit number)

46046369206697075516…82009300969045975041

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

9.209 × 10⁹⁸(99-digit number)

92092738413394151032…64018601938091950079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.209 × 10⁹⁸(99-digit number)

92092738413394151032…64018601938091950081

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

1.841 × 10⁹⁹(100-digit number)

18418547682678830206…28037203876183900159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.841 × 10⁹⁹(100-digit number)

18418547682678830206…28037203876183900161

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

3.683 × 10⁹⁹(100-digit number)

36837095365357660413…56074407752367800319

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 #113,469

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