Block #202,967

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/10/2013, 1:46:11 PM · Difficulty 9.8960 · 6,592,388 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

282e93003cc7477fec5d9d5d918afa5d4f79a837bcc1d64143692631f7124014

View on Chainz ↗

Height

#202,967

Difficulty

9.895988

Transactions

Size

2.64 KB

Version

Bits

09e55f72

Nonce

29,725

Timestamp

10/10/2013, 1:46:11 PM

Confirmations

6,592,388

Mined by

⛏️ P2SHAPEcDKBhiwmtCs4uPmnx1PYtaBbvmts2ty

Merkle Root

c76b2c9d101f20128ba3034f18748c888be97b6af1a1fd44c273ccc4aa1baa96

Transactions (3)

Coinbasecd5eb91cc595e7…d49cc92f74316d

1 in → 1 out10.2400 XPM109 B

APEcDKBh…bvmts2ty

83bdc9ac154a29…230a2e861cd465

19 in → 2 out174.0204 XPM2.26 KB

AWKpUf5f…S2RLN5dS AVCzsT1v…4jqWvChe

80a7b79a8883f5…03721798c96c18

1 in → 2 out10.2000 XPM192 B

ARdB18ae…36Uxuv5i AFz9fXym…wh4UqpkL

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.

2.211 × 10⁹³(94-digit number)

22115290537342442810…02701060411103000959

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

2.211 × 10⁹³(94-digit number)

22115290537342442810…02701060411103000959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.211 × 10⁹³(94-digit number)

22115290537342442810…02701060411103000961

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

4.423 × 10⁹³(94-digit number)

44230581074684885620…05402120822206001919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.423 × 10⁹³(94-digit number)

44230581074684885620…05402120822206001921

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

8.846 × 10⁹³(94-digit number)

88461162149369771240…10804241644412003839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.846 × 10⁹³(94-digit number)

88461162149369771240…10804241644412003841

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

1.769 × 10⁹⁴(95-digit number)

17692232429873954248…21608483288824007679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.769 × 10⁹⁴(95-digit number)

17692232429873954248…21608483288824007681

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

3.538 × 10⁹⁴(95-digit number)

35384464859747908496…43216966577648015359

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