Home/Chain Registry/Block #273,203

Block #273,203

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/25/2013, 4:32:22 PM · Difficulty 9.9543 · 6,518,732 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

600918badf68bbe22e7fe1a9443cd0b4af021e7131fbd79a3418b196b51d704a

View on Chainz ↗

Height

#273,203

Difficulty

9.954312

Transactions

Size

205 B

Version

Bits

09f44dd1

Nonce

70,809

Timestamp

11/25/2013, 4:32:22 PM

Confirmations

6,518,732

Merkle Root

8bbd2bb129d539179c0ee3a4627426254ba9397a36aa2f527cfe20ce8b7e6247

Transactions (1)

Coinbase8bbd2bb129d539…fe20ce8b7e6247

1 in → 1 out10.0800 XPM116 B

AcLBm5Z9…S683d7c3

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.

3.729 × 10⁹¹(92-digit number)

37295437855376899149…29571798471248511520

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

3.729 × 10⁹¹(92-digit number)

37295437855376899149…29571798471248511519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.729 × 10⁹¹(92-digit number)

37295437855376899149…29571798471248511521

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

7.459 × 10⁹¹(92-digit number)

74590875710753798299…59143596942497023039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.459 × 10⁹¹(92-digit number)

74590875710753798299…59143596942497023041

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

1.491 × 10⁹²(93-digit number)

14918175142150759659…18287193884994046079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.491 × 10⁹²(93-digit number)

14918175142150759659…18287193884994046081

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

2.983 × 10⁹²(93-digit number)

29836350284301519319…36574387769988092159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.983 × 10⁹²(93-digit number)

29836350284301519319…36574387769988092161

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

5.967 × 10⁹²(93-digit number)

59672700568603038639…73148775539976184319

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 273203

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 600918badf68bbe22e7fe1a9443cd0b4af021e7131fbd79a3418b196b51d704a

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 #273,203 on Chainz ↗