Block #430,549

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/5/2014, 1:52:37 PM · Difficulty 10.3446 · 6,386,208 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5c631dece9961929b485b12dacee96d5a0afba2cf57158962b4243757c902c67

View on Chainz ↗

Height

#430,549

Difficulty

10.344640

Transactions

Size

13.07 KB

Version

Bits

0a583a4f

Nonce

1,846,166

Timestamp

3/5/2014, 1:52:37 PM

Confirmations

6,386,208

Mined by

⛏️ P2SHANnadbTXF7bpEEbXNZsGZLTPRPHS3F7Ffn

Merkle Root

2ef0dc1e313c09d6e4d58eb13ff2dc73002c12c751edf1e554fc3ff7e8282377

Transactions (4)

Coinbasedfb2cf344979e9…93e8a085ee6d4d

1 in → 1 out9.4800 XPM109 B

ANnadbTX…HS3F7Ffn

99385d111fa716…11a3d9a9d15170

1 in → 1 out9.2900 XPM158 B

Aa7SCWJe…EEUE2cR6

30d6e525be22fe…f7a3eb4b2f6912

86 in → 2 out770.1782 XPM12.50 KB

AL2T2KCh…V5B1km4N AcvJDQ16…SRBpo1zS

053a4d96bd93cb…25e5b3d9a84d21

1 in → 2 out3.1463 XPM225 B

AGbSDyV6…bfYhtgWd AX84pGDZ…14NffaRP

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.

2.234 × 10⁹⁵(96-digit number)

22341416989271502492…72452174342635831199

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

2.234 × 10⁹⁵(96-digit number)

22341416989271502492…72452174342635831199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.234 × 10⁹⁵(96-digit number)

22341416989271502492…72452174342635831201

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

4.468 × 10⁹⁵(96-digit number)

44682833978543004985…44904348685271662399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.468 × 10⁹⁵(96-digit number)

44682833978543004985…44904348685271662401

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

8.936 × 10⁹⁵(96-digit number)

89365667957086009971…89808697370543324799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.936 × 10⁹⁵(96-digit number)

89365667957086009971…89808697370543324801

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

1.787 × 10⁹⁶(97-digit number)

17873133591417201994…79617394741086649599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.787 × 10⁹⁶(97-digit number)

17873133591417201994…79617394741086649601

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

3.574 × 10⁹⁶(97-digit number)

35746267182834403988…59234789482173299199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.574 × 10⁹⁶(97-digit number)

35746267182834403988…59234789482173299201

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

Block #430,549

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