Block #259,356

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/13/2013, 2:15:25 PM · Difficulty 9.9772 · 6,574,430 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dc961bdfbdeafbf74bfaf66335f0e9982465d2c87920f665568e0bde74136f3e

View on Chainz ↗

Height

#259,356

Difficulty

9.977184

Transactions

Size

1.74 KB

Version

Bits

09fa28b5

Nonce

68,465

Timestamp

11/13/2013, 2:15:25 PM

Confirmations

6,574,430

Mined by

⛏️ aRKANuKx9Kemb4q2j6b7vjmfuKrAuwm7nrBRq

Merkle Root

f8e292616d1d545ec0e94cbae3e1156d355786e1e3cf79d221c9abd6151bfcf1

Transactions (1)

Coinbasef8e292616d1d54…c9abd6151bfcf1

1 in → 48 out10.0100 XPM1.66 KB

ANuKx9Ke…wm7nrBRq AFqKfjez…qX9Ace3g AXDu24HR…L9o8sC5D AQtzUSwq…htAuF3yC AKDTDDtx…iqvw9cdY

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.

3.050 × 10⁹¹(92-digit number)

30507226423993713543…16594969416050498079

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

3.050 × 10⁹¹(92-digit number)

30507226423993713543…16594969416050498079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.050 × 10⁹¹(92-digit number)

30507226423993713543…16594969416050498081

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

6.101 × 10⁹¹(92-digit number)

61014452847987427086…33189938832100996159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.101 × 10⁹¹(92-digit number)

61014452847987427086…33189938832100996161

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

1.220 × 10⁹²(93-digit number)

12202890569597485417…66379877664201992319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.220 × 10⁹²(93-digit number)

12202890569597485417…66379877664201992321

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

2.440 × 10⁹²(93-digit number)

24405781139194970834…32759755328403984639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.440 × 10⁹²(93-digit number)

24405781139194970834…32759755328403984641

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

4.881 × 10⁹²(93-digit number)

48811562278389941669…65519510656807969279

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 #259,356

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