Block #251,346

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/8/2013, 11:28:28 PM · Difficulty 9.9698 · 6,559,286 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ded135f7a06575da380ad61005c7c9cf063ff42f1f80d9a16a280476f8aefcae

View on Chainz ↗

Height

#251,346

Difficulty

9.969803

Transactions

Size

2.04 KB

Version

Bits

09f84506

Nonce

25,016

Timestamp

11/8/2013, 11:28:28 PM

Confirmations

6,559,286

Mined by

⛏️ aR}sAQvGmFRtQf3eT6L4x2yptWr8fgxEKL8LoR

Merkle Root

f66b5f70f8c81646b37a28c04352722c71bbab1fb5715780e35d995cfdfffee6

Transactions (1)

Coinbasef66b5f70f8c816…5d995cfdfffee6

1 in → 57 out10.0300 XPM1.95 KB

AQvGmFRt…xEKL8LoR AQtzUSwq…htAuF3yC AKDTDDtx…iqvw9cdY ANo4YY1x…vnsPRDSU AJzWx2VD…j4ZSMit5

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.

1.634 × 10⁹⁹(100-digit number)

16345615840796110775…34211094459718251199

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

1.634 × 10⁹⁹(100-digit number)

16345615840796110775…34211094459718251199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.634 × 10⁹⁹(100-digit number)

16345615840796110775…34211094459718251201

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

3.269 × 10⁹⁹(100-digit number)

32691231681592221550…68422188919436502399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.269 × 10⁹⁹(100-digit number)

32691231681592221550…68422188919436502401

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

6.538 × 10⁹⁹(100-digit number)

65382463363184443101…36844377838873004799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.538 × 10⁹⁹(100-digit number)

65382463363184443101…36844377838873004801

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

1.307 × 10¹⁰⁰(101-digit number)

13076492672636888620…73688755677746009599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.307 × 10¹⁰⁰(101-digit number)

13076492672636888620…73688755677746009601

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

2.615 × 10¹⁰⁰(101-digit number)

26152985345273777240…47377511355492019199

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 #251,346

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