Block #275,522

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/26/2013, 6:01:01 PM · Difficulty 9.9610 · 6,541,324 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5dabdb2c21f9a47b4c398c69b29e0ebc7e735eca5d955b8397b3cfd4c5c90234

View on Chainz ↗

Height

#275,522

Difficulty

9.961013

Transactions

Size

803 B

Version

Bits

09f604ec

Nonce

26,181

Timestamp

11/26/2013, 6:01:01 PM

Confirmations

6,541,324

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

20b5b62b304ef792dd02475d160f9be3d588be503480427bf81c6abef2acceb9

Transactions (3)

Coinbase71d02d1c2d942b…aff30d022d685b

1 in → 1 out10.1000 XPM110 B

AeKNrjNj…1NEq95Ta

18c75211da5c43…d05b96da1dda6a

1 in → 2 out1.9985 XPM226 B

APvwbnm3…m8xCVXA1 APeD1DGy…su4FkMdy

71139dbe9a7cc2…341dfe4440519d

2 in → 2 out0.0306 XPM375 B

AVB5qatL…2JBaJVHh AVYVVYUJ…m8MefuGo

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.

2.638 × 10⁹⁹(100-digit number)

26388733633521893147…97468123031089602559

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

2.638 × 10⁹⁹(100-digit number)

26388733633521893147…97468123031089602559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.638 × 10⁹⁹(100-digit number)

26388733633521893147…97468123031089602561

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

5.277 × 10⁹⁹(100-digit number)

52777467267043786295…94936246062179205119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.277 × 10⁹⁹(100-digit number)

52777467267043786295…94936246062179205121

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

1.055 × 10¹⁰⁰(101-digit number)

10555493453408757259…89872492124358410239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.055 × 10¹⁰⁰(101-digit number)

10555493453408757259…89872492124358410241

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

2.111 × 10¹⁰⁰(101-digit number)

21110986906817514518…79744984248716820479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.111 × 10¹⁰⁰(101-digit number)

21110986906817514518…79744984248716820481

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

4.222 × 10¹⁰⁰(101-digit number)

42221973813635029036…59489968497433640959

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 #275,522

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