Home/Chain Registry/Block #257,620

Block #257,620

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/12/2013, 1:56:29 PM · Difficulty 9.9758 · 6,553,370 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cc0db3ea6cbd6a6da18cface2ebcfba3cc9724c9cc32b4c00a6c954f9d41e842

View on Chainz ↗

Height

#257,620

Difficulty

9.975838

Transactions

Size

457 B

Version

Bits

09f9d086

Nonce

16,872

Timestamp

11/12/2013, 1:56:29 PM

Confirmations

6,553,370

Merkle Root

7312107313f306b94230b93fc7c02a0d03ad1182a83b0c91fc249ddb80e9023e

Transactions (2)

Coinbase0466c2470afde7…430f729aba8d97

1 in → 2 out10.0400 XPM141 B

AKcbk49N…GJbKa7j1 AU6kq4CL…dQBLvxLp

ef8d16cf5a83ae…cc4c82fa6baebd

1 in → 2 out10.0300 XPM226 B

ASUFgEJz…aJrTqZmj ANkwR1gm…dSoJBgDe

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.

1.354 × 10⁹⁵(96-digit number)

13542090975070042077…82855133973329643880

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

1.354 × 10⁹⁵(96-digit number)

13542090975070042077…82855133973329643879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.354 × 10⁹⁵(96-digit number)

13542090975070042077…82855133973329643881

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

2.708 × 10⁹⁵(96-digit number)

27084181950140084154…65710267946659287759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.708 × 10⁹⁵(96-digit number)

27084181950140084154…65710267946659287761

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

5.416 × 10⁹⁵(96-digit number)

54168363900280168309…31420535893318575519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.416 × 10⁹⁵(96-digit number)

54168363900280168309…31420535893318575521

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

1.083 × 10⁹⁶(97-digit number)

10833672780056033661…62841071786637151039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.083 × 10⁹⁶(97-digit number)

10833672780056033661…62841071786637151041

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

2.166 × 10⁹⁶(97-digit number)

21667345560112067323…25682143573274302079

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 257620

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 cc0db3ea6cbd6a6da18cface2ebcfba3cc9724c9cc32b4c00a6c954f9d41e842

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 #257,620 on Chainz ↗

Block #257,620

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