Block #426,162

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/2/2014, 10:32:34 AM · Difficulty 10.3571 · 6,383,559 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6893f473f41bbb7242322816751014513573c7e04468af271fde2c40bee320a2

View on Chainz ↗

Height

#426,162

Difficulty

10.357072

Transactions

Size

1.63 KB

Version

Bits

0a5b690a

Nonce

20,633,878

Timestamp

3/2/2014, 10:32:34 AM

Confirmations

6,383,559

Mined by

⛏️ P2SHAameHBHe4kYi1iuLF9vyEHMYSJCFdmUsde

Merkle Root

a90c16fb083201758d0abdd36b3a9c0d89014805d8fcd79160753e97e725433f

Transactions (4)

Coinbase4cf63235de7744…bc9766e352ece0

1 in → 1 out9.3400 XPM109 B

AameHBHe…CFdmUsde

6afb142c2b2e55…d43ab1ccee4932

4 in → 1 out36.9000 XPM498 B

AXievGTY…wXGvxxSg

daa2c6bae4ed79…eb0f9fd6158cf4

1 in → 1 out3.9913 XPM192 B

AGvAR2n8…cCzbvv6m

4462324380abc1…6b8ef7a9a6af4c

2 in → 16 out18.6000 XPM783 B

AJ7bwxHw…vy276KPV AJTSZysw…vp9dVkhW ALRECLTt…diW9Y5Vu AMAhFBm2…B1MTCAzU AMTcH6rD…J5EReFoC

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.

8.942 × 10⁹⁵(96-digit number)

89421122993596506652…98644702084725154559

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

8.942 × 10⁹⁵(96-digit number)

89421122993596506652…98644702084725154559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.942 × 10⁹⁵(96-digit number)

89421122993596506652…98644702084725154561

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

1.788 × 10⁹⁶(97-digit number)

17884224598719301330…97289404169450309119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.788 × 10⁹⁶(97-digit number)

17884224598719301330…97289404169450309121

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

3.576 × 10⁹⁶(97-digit number)

35768449197438602661…94578808338900618239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.576 × 10⁹⁶(97-digit number)

35768449197438602661…94578808338900618241

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

7.153 × 10⁹⁶(97-digit number)

71536898394877205322…89157616677801236479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.153 × 10⁹⁶(97-digit number)

71536898394877205322…89157616677801236481

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

1.430 × 10⁹⁷(98-digit number)

14307379678975441064…78315233355602472959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.430 × 10⁹⁷(98-digit number)

14307379678975441064…78315233355602472961

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 #426,162

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