Block #266,892

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/20/2013, 7:29:11 PM · Difficulty 9.9601 · 6,528,832 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c8a15cb1110ed624384b742dd05c35f8b925e6bd24ccc5ccbeeaf8d039296f40

View on Chainz ↗

Height

#266,892

Difficulty

9.960128

Transactions

Size

563 B

Version

Bits

09f5caf4

Nonce

636,284

Timestamp

11/20/2013, 7:29:11 PM

Confirmations

6,528,832

Mined by

⛏️ P2SHAbGkvdxHZ4BVXfnK4PvSdcrNAUoihMdBXd

Merkle Root

a785e1ffa4e2e382b04253f5e9bc771ae2cd6692322b84f107acd6ff68b95430

Transactions (2)

Coinbasea8145b70ea1c19…2948bb6f58e19a

1 in → 1 out10.0800 XPM100 B

AbGkvdxH…oihMdBXd

ffb6744d375a3d…3e5e6eac43dfb2

2 in → 2 out5.6009 XPM373 B

AH3dDrPX…iXBYe8ZV ASrKPtxW…ULEuf4Cv

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.

5.652 × 10⁹⁴(95-digit number)

56529791228544339354…51014054514438794879

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

5.652 × 10⁹⁴(95-digit number)

56529791228544339354…51014054514438794879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.652 × 10⁹⁴(95-digit number)

56529791228544339354…51014054514438794881

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

1.130 × 10⁹⁵(96-digit number)

11305958245708867870…02028109028877589759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.130 × 10⁹⁵(96-digit number)

11305958245708867870…02028109028877589761

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

2.261 × 10⁹⁵(96-digit number)

22611916491417735741…04056218057755179519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.261 × 10⁹⁵(96-digit number)

22611916491417735741…04056218057755179521

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

4.522 × 10⁹⁵(96-digit number)

45223832982835471483…08112436115510359039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.522 × 10⁹⁵(96-digit number)

45223832982835471483…08112436115510359041

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

9.044 × 10⁹⁵(96-digit number)

90447665965670942967…16224872231020718079

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