Home/Chain Registry/Block #266,577

Block #266,577

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/20/2013, 1:28:57 PM · Difficulty 9.9605 · 6,525,895 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d2e25741e1a288beee9f3110220ac8953678e3dff7ac8d536a320dbbe82f3b59

View on Chainz ↗

Height

#266,577

Difficulty

9.960461

Transactions

Size

232 B

Version

Bits

09f5e0c9

Nonce

9,319

Timestamp

11/20/2013, 1:28:57 PM

Confirmations

6,525,895

Merkle Root

52f76cb5b934cd4c626eef1e5e43ea6c76f068bf24d4635507c74f3150db6e0c

Transactions (1)

Coinbase52f76cb5b934cd…c74f3150db6e0c

1 in → 2 out10.0600 XPM139 B

AKcbk49N…GJbKa7j1 ASNt3cJa…L5zCqAYM

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.

6.917 × 10¹⁰²(103-digit number)

69177876739445204052…25553589055365568000

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

6.917 × 10¹⁰²(103-digit number)

69177876739445204052…25553589055365567999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.917 × 10¹⁰²(103-digit number)

69177876739445204052…25553589055365568001

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

1.383 × 10¹⁰³(104-digit number)

13835575347889040810…51107178110731135999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.383 × 10¹⁰³(104-digit number)

13835575347889040810…51107178110731136001

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

2.767 × 10¹⁰³(104-digit number)

27671150695778081620…02214356221462271999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.767 × 10¹⁰³(104-digit number)

27671150695778081620…02214356221462272001

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

5.534 × 10¹⁰³(104-digit number)

55342301391556163241…04428712442924543999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.534 × 10¹⁰³(104-digit number)

55342301391556163241…04428712442924544001

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

1.106 × 10¹⁰⁴(105-digit number)

11068460278311232648…08857424885849087999

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.

View full Prime Chain Discovery page →

★☆☆☆☆

Rarity

CommonChain length 9

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

Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height

getblockhash 266577

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data

getblock d2e25741e1a288beee9f3110220ac8953678e3dff7ac8d536a320dbbe82f3b59

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help → Debug Window → Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #266,577 on Chainz ↗