Home/Chain Registry/Block #1,223,603

Block #1,223,603

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/5/2015, 7:52:08 PM · Difficulty 10.7414 · 5,567,511 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

71859bf3768741864aa92d484990418e0fae882d261b8e865153c4a9d6f58d25

View on Chainz ↗

Height

#1,223,603

Difficulty

10.741449

Transactions

Size

208 B

Version

Bits

0abdcf9f

Nonce

8,900,876

Timestamp

9/5/2015, 7:52:08 PM

Confirmations

5,567,511

Merkle Root

8a1856b365ed09dc90a8e26d83d06701c6e4cbac70865c86716e0d8a783c7e48

Transactions (1)

Coinbase8a1856b365ed09…6e0d8a783c7e48

1 in → 1 out8.6500 XPM116 B

AJCEY9yy…tg97E6zm

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.

3.932 × 10⁹⁸(99-digit number)

39329824040278040885…23472312877585530880

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

3.932 × 10⁹⁸(99-digit number)

39329824040278040885…23472312877585530879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.932 × 10⁹⁸(99-digit number)

39329824040278040885…23472312877585530881

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

7.865 × 10⁹⁸(99-digit number)

78659648080556081770…46944625755171061759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.865 × 10⁹⁸(99-digit number)

78659648080556081770…46944625755171061761

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

1.573 × 10⁹⁹(100-digit number)

15731929616111216354…93889251510342123519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.573 × 10⁹⁹(100-digit number)

15731929616111216354…93889251510342123521

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

3.146 × 10⁹⁹(100-digit number)

31463859232222432708…87778503020684247039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.146 × 10⁹⁹(100-digit number)

31463859232222432708…87778503020684247041

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

6.292 × 10⁹⁹(100-digit number)

62927718464444865416…75557006041368494079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.292 × 10⁹⁹(100-digit number)

62927718464444865416…75557006041368494081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

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 1223603

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 71859bf3768741864aa92d484990418e0fae882d261b8e865153c4a9d6f58d25

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 #1,223,603 on Chainz ↗