Block #262,250

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/16/2013, 3:56:50 PM · Difficulty 9.9692 · 6,545,779 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b2b0be8a96e14cd6c17cdb5724889e102ab3096d2a081f6c3791d5c288cda786

View on Chainz ↗

Height

#262,250

Difficulty

9.969227

Transactions

Size

1.54 KB

Version

Bits

09f81f40

Nonce

19,601

Timestamp

11/16/2013, 3:56:50 PM

Confirmations

6,545,779

Mined by

⛏️ jaRzAKfwt5JYHvbU43cJZsmFAbyqP2jsjT5QJQ

Merkle Root

edcdb1cebffe1ef2ae3ca99aab334c6678cbbee1b65fceddc627447c97a0c1c6

Transactions (1)

Coinbaseedcdb1cebffe1e…27447c97a0c1c6

1 in → 42 out10.0300 XPM1.46 KB

AKfwt5JY…jsjT5QJQ AFqKfjez…qX9Ace3g AQtzUSwq…htAuF3yC APZy8y6E…QZaGQjfp AN4KokSc…8oFYPA8o

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.

7.381 × 10⁹²(93-digit number)

73811364553331694450…29456118108107825759

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

7.381 × 10⁹²(93-digit number)

73811364553331694450…29456118108107825759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.381 × 10⁹²(93-digit number)

73811364553331694450…29456118108107825761

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

1.476 × 10⁹³(94-digit number)

14762272910666338890…58912236216215651519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.476 × 10⁹³(94-digit number)

14762272910666338890…58912236216215651521

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

2.952 × 10⁹³(94-digit number)

29524545821332677780…17824472432431303039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.952 × 10⁹³(94-digit number)

29524545821332677780…17824472432431303041

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

5.904 × 10⁹³(94-digit number)

59049091642665355560…35648944864862606079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.904 × 10⁹³(94-digit number)

59049091642665355560…35648944864862606081

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

1.180 × 10⁹⁴(95-digit number)

11809818328533071112…71297889729725212159

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 #262,250

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