Block #112,523

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/12/2013, 12:56:46 AM · Difficulty 9.7227 · 6,704,487 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bedf73ddf76d5531b79ae6a4460d3777f5e5927ce2965a53dfc184f60748035b

View on Chainz ↗

Height

#112,523

Difficulty

9.722684

Transactions

Size

472 B

Version

Bits

09b901d3

Nonce

353,765

Timestamp

8/12/2013, 12:56:46 AM

Confirmations

6,704,487

Mined by

⛏️ P2SHAJMLcfL7UBwWBsobasJJBQjqRvDLuWQs4o

Merkle Root

749585536415772b3919e33634e5aa66c9b1e4b3a06843509f72020d64d3bfb1

Transactions (2)

Coinbase25815ffae06f7e…26ca2a6097e072

1 in → 1 out10.5700 XPM109 B

AJMLcfL7…DLuWQs4o

32c15faa68f804…eee1f63358d04d

2 in → 1 out21.7500 XPM271 B

APug1zqH…wfikf34c

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.

1.672 × 10⁹⁹(100-digit number)

16721181416255377194…41355981266428330479

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

1.672 × 10⁹⁹(100-digit number)

16721181416255377194…41355981266428330479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.672 × 10⁹⁹(100-digit number)

16721181416255377194…41355981266428330481

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

3.344 × 10⁹⁹(100-digit number)

33442362832510754388…82711962532856660959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.344 × 10⁹⁹(100-digit number)

33442362832510754388…82711962532856660961

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

6.688 × 10⁹⁹(100-digit number)

66884725665021508776…65423925065713321919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.688 × 10⁹⁹(100-digit number)

66884725665021508776…65423925065713321921

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

1.337 × 10¹⁰⁰(101-digit number)

13376945133004301755…30847850131426643839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.337 × 10¹⁰⁰(101-digit number)

13376945133004301755…30847850131426643841

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

2.675 × 10¹⁰⁰(101-digit number)

26753890266008603510…61695700262853287679

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 #112,523

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