Block #244,162

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/4/2013, 5:08:28 PM · Difficulty 9.9626 · 6,572,719 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ecbe874b5d31cf21b5a1cf6ffc0ef1ab84ed933aab813f1dbd2c1029090fb6e6

View on Chainz ↗

Height

#244,162

Difficulty

9.962558

Transactions

Size

1.61 KB

Version

Bits

09f66a36

Nonce

140,164

Timestamp

11/4/2013, 5:08:28 PM

Confirmations

6,572,719

Mined by

⛏️ RwjARanXFdqZu3gw2gscjananFaiq2FNquU2w

Merkle Root

b6bbe8a089b26c4c1bd0ac40331874c62444e3f5d293fdc63adfdbe323279dcf

Transactions (1)

Coinbaseb6bbe8a089b26c…dfdbe323279dcf

1 in → 44 out10.0400 XPM1.52 KB

ARanXFdq…2FNquU2w AdnG9gQ7…N9B7mA2p ARpndEmc…Hg792kEk Aaf3CsqS…k1Eu3vmJ AQtzUSwq…htAuF3yC

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.

9.817 × 10⁹¹(92-digit number)

98170114863375226109…74101007708947256319

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

9.817 × 10⁹¹(92-digit number)

98170114863375226109…74101007708947256319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.817 × 10⁹¹(92-digit number)

98170114863375226109…74101007708947256321

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

1.963 × 10⁹²(93-digit number)

19634022972675045221…48202015417894512639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.963 × 10⁹²(93-digit number)

19634022972675045221…48202015417894512641

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

3.926 × 10⁹²(93-digit number)

39268045945350090443…96404030835789025279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.926 × 10⁹²(93-digit number)

39268045945350090443…96404030835789025281

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

7.853 × 10⁹²(93-digit number)

78536091890700180887…92808061671578050559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.853 × 10⁹²(93-digit number)

78536091890700180887…92808061671578050561

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

1.570 × 10⁹³(94-digit number)

15707218378140036177…85616123343156101119

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 #244,162

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