Block #211,637

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/15/2013, 7:41:56 PM · Difficulty 9.9171 · 6,597,607 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e83b90e8b69f5c47b584277aefb62e15cd53a163953c472622e4f3de8c5dbb48

View on Chainz ↗

Height

#211,637

Difficulty

9.917093

Transactions

Size

5.46 KB

Version

Bits

09eac6a3

Nonce

1,164,799,278

Timestamp

10/15/2013, 7:41:56 PM

Confirmations

6,597,607

Mined by

⛏️ :RATqDht7FFkigamgCG2ukx6XCzSxHD53DYv

Merkle Root

e58d0ef7398595659a7ae00944cf1047017d5d5ed163261a370bef36c9a64de9

Transactions (1)

Coinbasee58d0ef7398595…0bef36c9a64de9

1 in → 160 out10.0900 XPM5.37 KB

ATqDht7F…xHD53DYv AYpBMdDM…2HHyzmwW AeLaP1NX…SJ53Q2G7 AbdqpFgm…M8UVG4YE AZLULveC…eWSqxiAs

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.

1.435 × 10⁹⁴(95-digit number)

14351248164820617296…11731270510257072239

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

1.435 × 10⁹⁴(95-digit number)

14351248164820617296…11731270510257072239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.435 × 10⁹⁴(95-digit number)

14351248164820617296…11731270510257072241

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

2.870 × 10⁹⁴(95-digit number)

28702496329641234593…23462541020514144479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.870 × 10⁹⁴(95-digit number)

28702496329641234593…23462541020514144481

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

5.740 × 10⁹⁴(95-digit number)

57404992659282469186…46925082041028288959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.740 × 10⁹⁴(95-digit number)

57404992659282469186…46925082041028288961

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

1.148 × 10⁹⁵(96-digit number)

11480998531856493837…93850164082056577919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.148 × 10⁹⁵(96-digit number)

11480998531856493837…93850164082056577921

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

2.296 × 10⁹⁵(96-digit number)

22961997063712987674…87700328164113155839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.296 × 10⁹⁵(96-digit number)

22961997063712987674…87700328164113155841

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 #211,637

Cookie Preferences