Block #208,139

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/13/2013, 8:24:07 PM · Difficulty 9.9052 · 6,587,403 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ecaaf801d9d66b04d7b3c77136593af2ee37c2502a69229d8285b7f855627046

View on Chainz ↗

Height

#208,139

Difficulty

9.905187

Transactions

Size

1.86 KB

Version

Bits

09e7ba55

Nonce

18,304

Timestamp

10/13/2013, 8:24:07 PM

Confirmations

6,587,403

Mined by

⛏️ P2SHAHPLSWVdVVmfZ1Mw8oxTBdXzN3ZdicvSUu

Merkle Root

e1762db8af754af1498cddb5bc325d9c3e10a969677fdfb8a06061f89ce30026

Transactions (4)

Coinbaseba11e38586b4b5…e976a8d018b18a

1 in → 1 out10.2100 XPM109 B

AHPLSWVd…ZdicvSUu

81855ef63d9fde…3b3c6ecf6ea4eb

2 in → 5 out13.5899 XPM441 B

AYTEe3zv…dXqbD9BB AZqjMFvv…G8aw2zC8 ANvtpRa1…QjsraDJz Acs9SHrk…QJSB8SFG AGgdmQ5N…mxzmTyQX

4ea4e0f0c58589…47018bcb021d35

5 in → 5 out13.3328 XPM888 B

Abky7LZE…yGxK6CDj AZScJLrw…CpdqTxKC ANvtpRa1…QjsraDJz AQXUSoBL…CzbjKp8b AQ9iyTCP…XkfuTJPJ

fddc0e5dc35383…22ee30c263b1ef

2 in → 2 out0.0700 XPM375 B

AcUnFofG…kPAN33ZA AZF2cJG2…igRgeTi3

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.

1.552 × 10⁹²(93-digit number)

15522835339237463514…88180615026442175999

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

1.552 × 10⁹²(93-digit number)

15522835339237463514…88180615026442175999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.552 × 10⁹²(93-digit number)

15522835339237463514…88180615026442176001

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

3.104 × 10⁹²(93-digit number)

31045670678474927028…76361230052884351999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.104 × 10⁹²(93-digit number)

31045670678474927028…76361230052884352001

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

6.209 × 10⁹²(93-digit number)

62091341356949854056…52722460105768703999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.209 × 10⁹²(93-digit number)

62091341356949854056…52722460105768704001

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

1.241 × 10⁹³(94-digit number)

12418268271389970811…05444920211537407999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.241 × 10⁹³(94-digit number)

12418268271389970811…05444920211537408001

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

2.483 × 10⁹³(94-digit number)

24836536542779941622…10889840423074815999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.483 × 10⁹³(94-digit number)

24836536542779941622…10889840423074816001

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