Block #259,303

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/13/2013, 1:28:01 PM · Difficulty 9.9772 · 6,557,575 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

931893e6da8ceaa48c57315a7b58947ebc2f69c344b69d98a0984b07338c2eeb

View on Chainz ↗

Height

#259,303

Difficulty

9.977161

Transactions

Size

458 B

Version

Bits

09fa273d

Nonce

27,085

Timestamp

11/13/2013, 1:28:01 PM

Confirmations

6,557,575

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

5f2ed0a54b701b12670e987767dd07875d00b770d3326a630d681f35505369f9

Transactions (2)

Coinbase669aed7108a96e…926a026fc3f8de

1 in → 2 out10.0400 XPM142 B

AKcbk49N…GJbKa7j1 AHsw4d6U…EnM8UXNZ

8411eea7389054…dff6f764bcaf3f

1 in → 2 out109.6015 XPM226 B

AYbTqVEy…nc4cFxoC AHpQUrMQ…EeeBngpr

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.

4.031 × 10⁹⁴(95-digit number)

40313488713541273482…25410746860672350559

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

4.031 × 10⁹⁴(95-digit number)

40313488713541273482…25410746860672350559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.031 × 10⁹⁴(95-digit number)

40313488713541273482…25410746860672350561

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

8.062 × 10⁹⁴(95-digit number)

80626977427082546965…50821493721344701119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.062 × 10⁹⁴(95-digit number)

80626977427082546965…50821493721344701121

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

1.612 × 10⁹⁵(96-digit number)

16125395485416509393…01642987442689402239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.612 × 10⁹⁵(96-digit number)

16125395485416509393…01642987442689402241

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

3.225 × 10⁹⁵(96-digit number)

32250790970833018786…03285974885378804479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.225 × 10⁹⁵(96-digit number)

32250790970833018786…03285974885378804481

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

6.450 × 10⁹⁵(96-digit number)

64501581941666037572…06571949770757608959

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 #259,303

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