Block #205,545

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/12/2013, 5:35:15 AM · Difficulty 9.8999 · 6,604,752 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

aa3ee9855133a3d571a7e8024e532bd8cff714aecd873c7ba0b3107f5e0f3910

View on Chainz ↗

Height

#205,545

Difficulty

9.899937

Transactions

Size

2.65 KB

Version

Bits

09e6623e

Nonce

356,499

Timestamp

10/12/2013, 5:35:15 AM

Confirmations

6,604,752

Mined by

⛏️ P2SHAVo4nLsoeusQq4YcpcTodgTaU3X8R3wdJY

Merkle Root

71c60a37d5c077c5aaf5104b9d80c4a2ff7c198837562dc00f2f2dc329572f85

Transactions (4)

Coinbase0c1ba3a7fe5f0b…e62f821b6ea871

1 in → 1 out10.2300 XPM109 B

AVo4nLso…X8R3wdJY

d6fc670e96fca5…7cf34e376ee19d

6 in → 2 out1399.8381 XPM968 B

AG9WR1jV…LqMLAzVe AMyK1rVd…9RBG9Tb4

1e3b4c8c8cd554…09bf9e137b2d46

6 in → 5 out12.0115 XPM1.04 KB

ANUwx8Nr…UTHbJ8dG AQVTXcXa…maKX6Qn7 AGMoGuHf…jtm7BGfn ASPNJf9F…sxn5eqGg AakRgPRB…wm9M2NkU

8b5829663e2747…aaed14be1c86de

2 in → 5 out11.0126 XPM476 B

AGMoGuHf…jtm7BGfn AakRgPRB…wm9M2NkU AUAJWg1o…eSCTqCot AVHcAXsf…3WhJsTgh ASPNJf9F…sxn5eqGg

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.

2.457 × 10⁹²(93-digit number)

24577110751871454977…33211763454815146799

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

2.457 × 10⁹²(93-digit number)

24577110751871454977…33211763454815146799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.457 × 10⁹²(93-digit number)

24577110751871454977…33211763454815146801

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

4.915 × 10⁹²(93-digit number)

49154221503742909954…66423526909630293599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.915 × 10⁹²(93-digit number)

49154221503742909954…66423526909630293601

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

9.830 × 10⁹²(93-digit number)

98308443007485819908…32847053819260587199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.830 × 10⁹²(93-digit number)

98308443007485819908…32847053819260587201

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

1.966 × 10⁹³(94-digit number)

19661688601497163981…65694107638521174399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.966 × 10⁹³(94-digit number)

19661688601497163981…65694107638521174401

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

3.932 × 10⁹³(94-digit number)

39323377202994327963…31388215277042348799

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 #205,545

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