Block #200,553

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/9/2013, 2:14:54 AM · Difficulty 9.8898 · 6,609,300 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b57cc59410079f9099b17c02e264ac1855926bb7911c74f44f37420eba69bf2f

View on Chainz ↗

Height

#200,553

Difficulty

9.889753

Transactions

Size

4.53 KB

Version

Bits

09e3c6d7

Nonce

1,164,776,413

Timestamp

10/9/2013, 2:14:54 AM

Confirmations

6,609,300

Mined by

⛏️ iRTAHo7y676AfFQ6SvV4xk8W7pEhQHnay4JgM

Merkle Root

dc00aaff2b3131ac9654b6ce7896e9e906e0eebba0ddc676b02a9b69688fd3b8

Transactions (1)

Coinbasedc00aaff2b3131…2a9b69688fd3b8

1 in → 132 out10.1600 XPM4.44 KB

AHo7y676…Hnay4JgM AcMPa5Yh…j5yHgkwm AMywVFvp…4C9akwUw APHpC8Ek…M5FHs6c7 Aei2d9CH…1JreaJ9w

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.

2.462 × 10⁹³(94-digit number)

24627535460425110801…86613877786833188179

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

2.462 × 10⁹³(94-digit number)

24627535460425110801…86613877786833188179

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.462 × 10⁹³(94-digit number)

24627535460425110801…86613877786833188181

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

4.925 × 10⁹³(94-digit number)

49255070920850221602…73227755573666376359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.925 × 10⁹³(94-digit number)

49255070920850221602…73227755573666376361

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

9.851 × 10⁹³(94-digit number)

98510141841700443205…46455511147332752719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.851 × 10⁹³(94-digit number)

98510141841700443205…46455511147332752721

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

1.970 × 10⁹⁴(95-digit number)

19702028368340088641…92911022294665505439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.970 × 10⁹⁴(95-digit number)

19702028368340088641…92911022294665505441

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

3.940 × 10⁹⁴(95-digit number)

39404056736680177282…85822044589331010879

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 #200,553

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