Block #266,004

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/20/2013, 2:25:44 AM · Difficulty 9.9612 · 6,551,947 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

169ad279949e89938bf50f73b024daa465476070a1c1cfa86c0544e872830d26

View on Chainz ↗

Height

#266,004

Difficulty

9.961155

Transactions

Size

683 B

Version

Bits

09f60e40

Nonce

27,797

Timestamp

11/20/2013, 2:25:44 AM

Confirmations

6,551,947

Mined by

⛏️ P2SHAdGRRh1eP4JFvQMqy7y2pLsryDQmctLb24

Merkle Root

ad234ed3aaa41cbef2cba8dc69ec307f1c8ff43c9a9ffe7659a5b68de032d4ec

Transactions (3)

Coinbase061546d519d869…af007aa524c007

1 in → 2 out10.0800 XPM139 B

AdGRRh1e…QmctLb24 AKNbfPoc…jfkpwAyL

201ce90bde4b67…731ec6551344dc

1 in → 2 out2618.2403 XPM226 B

AWGubD26…NiAqAqHV AUcxdpw3…4rjPAyta

7184d66202adfb…e4bbe821332e04

1 in → 2 out506.8008 XPM226 B

AcCqGHRL…62hQczR6 APEuzbJk…XE22L38D

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.

2.218 × 10⁹⁹(100-digit number)

22180986582793434407…06411385790002547199

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

2.218 × 10⁹⁹(100-digit number)

22180986582793434407…06411385790002547199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.218 × 10⁹⁹(100-digit number)

22180986582793434407…06411385790002547201

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

4.436 × 10⁹⁹(100-digit number)

44361973165586868815…12822771580005094399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.436 × 10⁹⁹(100-digit number)

44361973165586868815…12822771580005094401

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

8.872 × 10⁹⁹(100-digit number)

88723946331173737631…25645543160010188799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.872 × 10⁹⁹(100-digit number)

88723946331173737631…25645543160010188801

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

1.774 × 10¹⁰⁰(101-digit number)

17744789266234747526…51291086320020377599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.774 × 10¹⁰⁰(101-digit number)

17744789266234747526…51291086320020377601

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

3.548 × 10¹⁰⁰(101-digit number)

35489578532469495052…02582172640040755199

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 #266,004

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