Block #203,650

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/10/2013, 11:53:51 PM · Difficulty 9.8976 · 6,623,463 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e10eb6128564db2a2378ed5ff49e86bb051114ffbdc55e3d3881033edce860a7

View on Chainz ↗

Height

#203,650

Difficulty

9.897552

Transactions

Size

538 B

Version

Bits

09e5c5f0

Nonce

122,479

Timestamp

10/10/2013, 11:53:51 PM

Confirmations

6,623,463

Mined by

⛏️ P2SHAQrHEruQacjAeSWB1Yy2xckojBnyCdLbgQ

Merkle Root

7b4d16ed697e714c1325ac74896325c61bd2f6c1a7a681f66d726aa9dd11ec33

Transactions (2)

Coinbasec96801f4b76475…31fe117d4451c4

1 in → 1 out10.2005 XPM109 B

AQrHEruQ…nyCdLbgQ

1ddfca864794b5…b480d969e1ee1f

2 in → 1 out40.0000 XPM340 B

AbC36iz9…rPhN8kHy

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.

3.059 × 10⁹²(93-digit number)

30596145200330192817…45957388364149446799

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

3.059 × 10⁹²(93-digit number)

30596145200330192817…45957388364149446799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.059 × 10⁹²(93-digit number)

30596145200330192817…45957388364149446801

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

6.119 × 10⁹²(93-digit number)

61192290400660385635…91914776728298893599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.119 × 10⁹²(93-digit number)

61192290400660385635…91914776728298893601

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

1.223 × 10⁹³(94-digit number)

12238458080132077127…83829553456597787199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.223 × 10⁹³(94-digit number)

12238458080132077127…83829553456597787201

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

2.447 × 10⁹³(94-digit number)

24476916160264154254…67659106913195574399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.447 × 10⁹³(94-digit number)

24476916160264154254…67659106913195574401

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

4.895 × 10⁹³(94-digit number)

48953832320528308508…35318213826391148799

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 #203,650

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