Block #205,611

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/12/2013, 6:42:16 AM · Difficulty 9.8999 · 6,603,838 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fd2049c94cb786aff7d91f43f70a152d5d5768bcfb8dc857c06b1f07eb105343

View on Chainz ↗

Height

#205,611

Difficulty

9.899891

Transactions

Size

4.02 KB

Version

Bits

09e65f3c

Nonce

97,044

Timestamp

10/12/2013, 6:42:16 AM

Confirmations

6,603,838

Mined by

⛏️ P2SHAXtUHczob3NNdpiGvxAE1JUJfgKe72YFw4

Merkle Root

a8297d407646dc14ce13fe0cc374c4d942f4c5fbdfb3d7d5e50b4333bc451d82

Transactions (2)

Coinbasee383e182d79492…0606afc4ade0b4

1 in → 1 out10.2300 XPM110 B

AXtUHczo…Ke72YFw4

f2176da3230d27…a92a81eb553c52

34 in → 1 out347.3374 XPM3.82 KB

AbxSykSg…BX71twYi

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.

7.044 × 10⁹⁵(96-digit number)

70442417252024178050…04259386311578382079

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

7.044 × 10⁹⁵(96-digit number)

70442417252024178050…04259386311578382079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.044 × 10⁹⁵(96-digit number)

70442417252024178050…04259386311578382081

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

1.408 × 10⁹⁶(97-digit number)

14088483450404835610…08518772623156764159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.408 × 10⁹⁶(97-digit number)

14088483450404835610…08518772623156764161

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

2.817 × 10⁹⁶(97-digit number)

28176966900809671220…17037545246313528319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.817 × 10⁹⁶(97-digit number)

28176966900809671220…17037545246313528321

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

5.635 × 10⁹⁶(97-digit number)

56353933801619342440…34075090492627056639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.635 × 10⁹⁶(97-digit number)

56353933801619342440…34075090492627056641

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

1.127 × 10⁹⁷(98-digit number)

11270786760323868488…68150180985254113279

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 #205,611

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