Block #206,213

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/12/2013, 4:10:48 PM · Difficulty 9.9006 · 6,600,513 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c23a1959787a7094f4d835b5f43c775d94e68241c5d47491dce25a68bc3b44de

View on Chainz ↗

Height

#206,213

Difficulty

9.900618

Transactions

Size

1.64 KB

Version

Bits

09e68eef

Nonce

59,367

Timestamp

10/12/2013, 4:10:48 PM

Confirmations

6,600,513

Mined by

⛏️ P2SHAR5g4Sx1Eamqdi1GNxxx5rDBJspU8wgiSs

Merkle Root

a7a42347db6aa18e15b7395f12db1a53e7b38ed5bcd08d6c5278f5aa92b06621

Transactions (5)

Coinbase0345f848b754d8…ca87f1f8ff9d2f

1 in → 1 out10.2400 XPM109 B

AR5g4Sx1…pU8wgiSs

69bd7ebd0107dd…ea597f4a2df6f7

2 in → 7 out20.4110 XPM476 B

AFq51nP4…FqYfXapg Abky7LZE…yGxK6CDj ANvtpRa1…QjsraDJz ATxhwXQd…2i75kbKH ALd5yTY2…vgfAFVPZ

2eca8aff45bcc5…4d8094b8a4098e

2 in → 5 out12.8859 XPM441 B

AV25sm8S…BeQnNFks ANvtpRa1…QjsraDJz AeA7UJdg…Ko6jDkad ARHxzQXx…u6GK5dN8 AcxdZz5Z…yr89WZt1

41a9349b4e9f3c…48092f65288fe0

1 in → 2 out10.1800 XPM191 B

ANvtpRa1…QjsraDJz AQXUSoBL…CzbjKp8b

98113e661ba55e…f8012f10b77cd7

2 in → 2 out3.0114 XPM376 B

ASvjCDwn…7X5sWvKn AMmRqPsz…jZZeYEFU

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.

3.760 × 10⁹³(94-digit number)

37607709407856032389…07712881461169862199

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

3.760 × 10⁹³(94-digit number)

37607709407856032389…07712881461169862199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.760 × 10⁹³(94-digit number)

37607709407856032389…07712881461169862201

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

7.521 × 10⁹³(94-digit number)

75215418815712064779…15425762922339724399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.521 × 10⁹³(94-digit number)

75215418815712064779…15425762922339724401

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

1.504 × 10⁹⁴(95-digit number)

15043083763142412955…30851525844679448799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.504 × 10⁹⁴(95-digit number)

15043083763142412955…30851525844679448801

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

3.008 × 10⁹⁴(95-digit number)

30086167526284825911…61703051689358897599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.008 × 10⁹⁴(95-digit number)

30086167526284825911…61703051689358897601

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

6.017 × 10⁹⁴(95-digit number)

60172335052569651823…23406103378717795199

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #206,213

Cookie Preferences