Block #269,396

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/23/2013, 2:37:33 AM · Difficulty 9.9534 · 6,540,325 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1d5c6c9dbd541ede3f7746e262c0fd39464b3604c9154982217805d6b02593fe

View on Chainz ↗

Height

#269,396

Difficulty

9.953359

Transactions

Size

1.32 KB

Version

Bits

09f40f52

Nonce

118,029

Timestamp

11/23/2013, 2:37:33 AM

Confirmations

6,540,325

Mined by

⛏️ P2SHANWrHiAp1jAKM5aGHVgFxnabiNY2WAv4pT

Merkle Root

114389bedd0b386ad9aec79f0b657a403284dd53858c68233cbbb799fbcca442

Transactions (4)

Coinbased123ea57784ab6…d27b1e7dbc1343

1 in → 1 out10.1100 XPM109 B

ANWrHiAp…Y2WAv4pT

41a359248c1e78…d08c6743486494

1 in → 2 out42.1780 XPM226 B

AHVKXRoy…Q1PLkbEz AbKaEUmf…ScYsqksX

dd1c3d49a013be…ff03f6be558243

4 in → 3 out6.5463 XPM703 B

AeEfsV8M…YKaWhQ3f AeKNrjNj…1NEq95Ta AcADmAoe…8iNnoMzB

d5d203e2aa0225…a436e5567b10a3

1 in → 2 out2.8459 XPM227 B

AUCxxzqx…jSaqy9yS APhYzr2y…2dVWHMCN

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.

5.714 × 10⁹²(93-digit number)

57149513442980881051…86451176642971899199

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

5.714 × 10⁹²(93-digit number)

57149513442980881051…86451176642971899199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.714 × 10⁹²(93-digit number)

57149513442980881051…86451176642971899201

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

1.142 × 10⁹³(94-digit number)

11429902688596176210…72902353285943798399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.142 × 10⁹³(94-digit number)

11429902688596176210…72902353285943798401

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

2.285 × 10⁹³(94-digit number)

22859805377192352420…45804706571887596799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.285 × 10⁹³(94-digit number)

22859805377192352420…45804706571887596801

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

4.571 × 10⁹³(94-digit number)

45719610754384704841…91609413143775193599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.571 × 10⁹³(94-digit number)

45719610754384704841…91609413143775193601

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

9.143 × 10⁹³(94-digit number)

91439221508769409682…83218826287550387199

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 #269,396

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