Block #259,281

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/13/2013, 1:04:56 PM · Difficulty 9.9772 · 6,533,551 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5bdf98766be6c14dd5dd836fb500c02bf74a4d427d11a2a50d11e0d57e821982

View on Chainz ↗

Height

#259,281

Difficulty

9.977164

Transactions

Size

423 B

Version

Bits

09fa276b

Nonce

44,083

Timestamp

11/13/2013, 1:04:56 PM

Confirmations

6,533,551

Merkle Root

c6dbd056501bfb0f35005e74eb49971b97b36db7a23caf49809d24c5146b1a93

Transactions (2)

Coinbase6212c57b03f890…42d8966ec22207

1 in → 1 out10.0400 XPM109 B

AWQfuoTC…GowsLP2U

229658ad2b04c4…5b3e9f9f8d8720

1 in → 2 out109.6677 XPM225 B

AepcsVct…pfX6Xj7s AZdmkNt9…Dk8ffFeU

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.

4.886 × 10⁹¹(92-digit number)

48862117663945558552…13824032437161119999

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

4.886 × 10⁹¹(92-digit number)

48862117663945558552…13824032437161119999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.886 × 10⁹¹(92-digit number)

48862117663945558552…13824032437161120001

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

9.772 × 10⁹¹(92-digit number)

97724235327891117105…27648064874322239999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.772 × 10⁹¹(92-digit number)

97724235327891117105…27648064874322240001

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

1.954 × 10⁹²(93-digit number)

19544847065578223421…55296129748644479999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.954 × 10⁹²(93-digit number)

19544847065578223421…55296129748644480001

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

3.908 × 10⁹²(93-digit number)

39089694131156446842…10592259497288959999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.908 × 10⁹²(93-digit number)

39089694131156446842…10592259497288960001

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

7.817 × 10⁹²(93-digit number)

78179388262312893684…21184518994577919999

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