Block #201,035

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/9/2013, 9:27:42 AM · Difficulty 9.8909 · 6,597,664 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1f8f00abb5ea99f4d4722ff0ea590817d8aff98e338952b4daa12fdea211f342

View on Chainz ↗

Height

#201,035

Difficulty

9.890912

Transactions

Size

5.01 KB

Version

Bits

09e412d1

Nonce

11,503

Timestamp

10/9/2013, 9:27:42 AM

Confirmations

6,597,664

Mined by

⛏️ P2SHAJar1HaysU6GcxoyUUuARaqiAgo3cZCX5R

Merkle Root

2e703f393844793bda8da6746f21d4be75bd941a58fe3f5c64e78a3318548be9

Transactions (2)

Coinbase643fcf16754804…3636256db9ad7e

1 in → 1 out10.2600 XPM109 B

AJar1Hay…o3cZCX5R

c9f233cc2b6371…690afff151d415

39 in → 2 out280.0591 XPM4.82 KB

ASDnv9Bm…izV9PQcR AXEkn78K…DofzmbKq

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.

5.054 × 10⁹²(93-digit number)

50543852914243597580…43222873207459228079

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

5.054 × 10⁹²(93-digit number)

50543852914243597580…43222873207459228079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.054 × 10⁹²(93-digit number)

50543852914243597580…43222873207459228081

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

1.010 × 10⁹³(94-digit number)

10108770582848719516…86445746414918456159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.010 × 10⁹³(94-digit number)

10108770582848719516…86445746414918456161

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

2.021 × 10⁹³(94-digit number)

20217541165697439032…72891492829836912319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.021 × 10⁹³(94-digit number)

20217541165697439032…72891492829836912321

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

4.043 × 10⁹³(94-digit number)

40435082331394878064…45782985659673824639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.043 × 10⁹³(94-digit number)

40435082331394878064…45782985659673824641

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

8.087 × 10⁹³(94-digit number)

80870164662789756129…91565971319347649279

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