Block #212,449

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/16/2013, 7:21:18 AM · Difficulty 9.9189 · 6,596,657 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e53d5695c7ed949a72caa897bbf0ce134f4425893f532b9cab41e937580e889b

View on Chainz ↗

Height

#212,449

Difficulty

9.918901

Transactions

Size

9.10 KB

Version

Bits

09eb3d1d

Nonce

94,384

Timestamp

10/16/2013, 7:21:18 AM

Confirmations

6,596,657

Mined by

⛏️ P2SHATuGr3cNJYyWx3Pyz9rYLTVV6BBBXfaBRV

Merkle Root

effdd501529463a6e04ff20fb5f75586ec45523d61a9411830476d8885e5b0b5

Transactions (4)

Coinbase7101b6a102849a…2ce2d2f40b734b

1 in → 1 out10.3000 XPM109 B

ATuGr3cN…BBXfaBRV

cbd4093067346e…cafb1bfe01c60f

6 in → 2 out337.7705 XPM966 B

AJ8DKCU1…rW1aNQg5 AcCgsTMF…biYCTP8b

a443437e173aaf…5228e2fbcd48b7

46 in → 2 out299.9088 XPM6.73 KB

AaQoUeZ2…psLPdhrd AKPsK7hq…JimrEcdU

5890a5a626796a…89778e931d2194

8 in → 2 out84.2727 XPM1.23 KB

AGgmT2uV…68qGLfJD ALpthvGg…D1g5z4CT

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.

3.467 × 10⁹³(94-digit number)

34671384378189931874…02778582944614942279

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

3.467 × 10⁹³(94-digit number)

34671384378189931874…02778582944614942279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.467 × 10⁹³(94-digit number)

34671384378189931874…02778582944614942281

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

6.934 × 10⁹³(94-digit number)

69342768756379863748…05557165889229884559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.934 × 10⁹³(94-digit number)

69342768756379863748…05557165889229884561

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

1.386 × 10⁹⁴(95-digit number)

13868553751275972749…11114331778459769119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.386 × 10⁹⁴(95-digit number)

13868553751275972749…11114331778459769121

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

2.773 × 10⁹⁴(95-digit number)

27737107502551945499…22228663556919538239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.773 × 10⁹⁴(95-digit number)

27737107502551945499…22228663556919538241

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

5.547 × 10⁹⁴(95-digit number)

55474215005103890998…44457327113839076479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.547 × 10⁹⁴(95-digit number)

55474215005103890998…44457327113839076481

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 #212,449

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