Block #285,429

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/30/2013, 12:05:32 PM · Difficulty 9.9843 · 6,518,128 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2db3c83ba85907e9cc5135a232628f2b745c1fa6d04ee9eceb51b2670d3d2697

View on Chainz ↗

Height

#285,429

Difficulty

9.984251

Transactions

Size

1.83 KB

Version

Bits

09fbf7df

Nonce

34,001

Timestamp

11/30/2013, 12:05:32 PM

Confirmations

6,518,128

Mined by

⛏️ ZaRAd9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

d4d02c783b2bc2a3cdbfc70723598159265b0b2748bdfce1313db73bf8a9b933

Transactions (2)

Coinbase1e577c77532959…08a6c53f80dbf5

1 in → 29 out10.0000 XPM1.02 KB

Ad9pSzHt…cpJ3y2zz AWhjURsQ…4R3DuPWU AbtgNzNb…9Atvu81w AXfjXSqG…R4XeNmLa AWNBNy6T…oHicAMKv

e2a35f0871fab0…0ea9a897037b2c

4 in → 8 out40.3700 XPM738 B

AGvhERyb…UeCkzWbg AeKNrjNj…1NEq95Ta AKL6bdQp…hNjj8m2T AXA2CgAY…sjcwKJeP AHnSFGh9…igeoL2xU

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.

5.610 × 10⁹²(93-digit number)

56107639333304498886…46516080899460556799

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

5.610 × 10⁹²(93-digit number)

56107639333304498886…46516080899460556799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.610 × 10⁹²(93-digit number)

56107639333304498886…46516080899460556801

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

1.122 × 10⁹³(94-digit number)

11221527866660899777…93032161798921113599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.122 × 10⁹³(94-digit number)

11221527866660899777…93032161798921113601

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

2.244 × 10⁹³(94-digit number)

22443055733321799554…86064323597842227199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.244 × 10⁹³(94-digit number)

22443055733321799554…86064323597842227201

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

4.488 × 10⁹³(94-digit number)

44886111466643599109…72128647195684454399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.488 × 10⁹³(94-digit number)

44886111466643599109…72128647195684454401

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

8.977 × 10⁹³(94-digit number)

89772222933287198219…44257294391368908799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.977 × 10⁹³(94-digit number)

89772222933287198219…44257294391368908801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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