Block #275,614

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/26/2013, 7:02:20 PM · Difficulty 9.9613 · 6,520,832 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

60c3bd85d29311b63f7924965400d6f686ccce7a0e3287c0618a4b906ee4b4cb

View on Chainz ↗

Height

#275,614

Difficulty

9.961256

Transactions

Size

3.19 KB

Version

Bits

09f614dc

Nonce

108,957

Timestamp

11/26/2013, 7:02:20 PM

Confirmations

6,520,832

Mined by

⛏️ 4aRAV38iKvBznaZFv4Phwqv3rh894ThTfXfGh

Merkle Root

5ac3d68ae86794cdea5345978e587633e665d855e26130b244ca64f909b140fc

Transactions (4)

Coinbaseaf87742cc59199…0042838f452aaf

1 in → 28 out10.0400 XPM1015 B

AV38iKvB…ThTfXfGh ANt4qZJR…v3reHqRo Aai6TNLM…kQf2QbQd AN8nUzff…YcDfRDQ2 Ac5sZcdP…kzV4eckG

85577a31796c35…eed35f218c5fed

3 in → 2 out19.8240 XPM522 B

AbP53inK…ugAepqUL ALHpSvM2…RUFnvKbJ

a1d55761736370…8e4ba0bda4f832

6 in → 2 out59.4187 XPM965 B

ALi7jgUj…EX5HRqDw AMMLTNA6…n16Q2F5o

622de120818258…24dc84ef02894d

4 in → 2 out2.7470 XPM671 B

AbpDNWqV…yQGH7THk AJVamtLF…Qkiptsu9

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.

5.386 × 10⁹¹(92-digit number)

53860090561577688113…56658998921811149279

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

5.386 × 10⁹¹(92-digit number)

53860090561577688113…56658998921811149279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.386 × 10⁹¹(92-digit number)

53860090561577688113…56658998921811149281

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

1.077 × 10⁹²(93-digit number)

10772018112315537622…13317997843622298559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.077 × 10⁹²(93-digit number)

10772018112315537622…13317997843622298561

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

2.154 × 10⁹²(93-digit number)

21544036224631075245…26635995687244597119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.154 × 10⁹²(93-digit number)

21544036224631075245…26635995687244597121

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

4.308 × 10⁹²(93-digit number)

43088072449262150490…53271991374489194239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.308 × 10⁹²(93-digit number)

43088072449262150490…53271991374489194241

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

8.617 × 10⁹²(93-digit number)

86176144898524300981…06543982748978388479

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