Block #391,212

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/5/2014, 4:05:34 PM · Difficulty 10.4299 · 6,418,236 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c0c3960d6ab5448e7a6314cf7aef6ff1b684e3a96c6b13b004c9162e9e397068

View on Chainz ↗

Height

#391,212

Difficulty

10.429907

Transactions

Size

2.68 KB

Version

Bits

0a6e0e64

Nonce

52,826

Timestamp

2/5/2014, 4:05:34 PM

Confirmations

6,418,236

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

0876f40b2843302de2dbec24fe3045584f0c1a5f536b93ae3b643fb5aa6d0cfe

Transactions (3)

Coinbaseca116a012ab2d6…72631dbcae0fa6

1 in → 1 out9.2200 XPM116 B

AbwWkWZt…kawDhufa

9aa13fb0be6878…df2924170dc913

7 in → 2 out21.0447 XPM1.09 KB

AMa9HmhX…5Gu8psXK ALCceKkR…x3cwsng5

7077b4fca666d3…4e1ebd81486b29

7 in → 17 out55.4482 XPM1.39 KB

AeKNrjNj…1NEq95Ta AMnNFUVt…um9Nn6ba AUkLzhdx…6FJGTCiB AX1pRuRy…1MbZNhnM AJTnJPkG…6HTSvS8F

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.

6.305 × 10⁹⁷(98-digit number)

63053840642704938086…76096389003221710799

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

6.305 × 10⁹⁷(98-digit number)

63053840642704938086…76096389003221710799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.305 × 10⁹⁷(98-digit number)

63053840642704938086…76096389003221710801

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

1.261 × 10⁹⁸(99-digit number)

12610768128540987617…52192778006443421599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.261 × 10⁹⁸(99-digit number)

12610768128540987617…52192778006443421601

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

2.522 × 10⁹⁸(99-digit number)

25221536257081975234…04385556012886843199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.522 × 10⁹⁸(99-digit number)

25221536257081975234…04385556012886843201

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

5.044 × 10⁹⁸(99-digit number)

50443072514163950469…08771112025773686399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.044 × 10⁹⁸(99-digit number)

50443072514163950469…08771112025773686401

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

1.008 × 10⁹⁹(100-digit number)

10088614502832790093…17542224051547372799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.008 × 10⁹⁹(100-digit number)

10088614502832790093…17542224051547372801

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 #391,212

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