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Block #410,757

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/19/2014, 7:07:22 AM · Difficulty 10.4293 · 6,385,373 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e09679d90b7856ff344f76e9c8f06a48345e914e53cd3d732aa066bf1b116e02

View on Chainz ↗

Height

#410,757

Difficulty

10.429290

Transactions

Size

642 B

Version

Bits

0a6de5ed

Nonce

256,175

Timestamp

2/19/2014, 7:07:22 AM

Confirmations

6,385,373

Merkle Root

c57d5c6981bdfb3004022920d2379f13061f0774a229fe7e3aeb2388c977a308

Transactions (2)

Coinbaseee166d7636a8ac…1b889a83162ec4

1 in → 1 out9.1900 XPM110 B

AeKNrjNj…1NEq95Ta

cf174146baaf32…4fd7bed4bb0d43

2 in → 6 out18.3800 XPM442 B

APaJvQ3G…25PSkPEZ AJCY4vXj…F6vHctZE AeKNrjNj…1NEq95Ta Acag3ba1…JAWgJwcR AJm7Bato…CGjsUjn8

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.

6.860 × 10⁹⁴(95-digit number)

68601785863725752893…48170206531737045340

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

6.860 × 10⁹⁴(95-digit number)

68601785863725752893…48170206531737045339

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.860 × 10⁹⁴(95-digit number)

68601785863725752893…48170206531737045341

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

1.372 × 10⁹⁵(96-digit number)

13720357172745150578…96340413063474090679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.372 × 10⁹⁵(96-digit number)

13720357172745150578…96340413063474090681

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

2.744 × 10⁹⁵(96-digit number)

27440714345490301157…92680826126948181359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.744 × 10⁹⁵(96-digit number)

27440714345490301157…92680826126948181361

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

5.488 × 10⁹⁵(96-digit number)

54881428690980602315…85361652253896362719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.488 × 10⁹⁵(96-digit number)

54881428690980602315…85361652253896362721

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

1.097 × 10⁹⁶(97-digit number)

10976285738196120463…70723304507792725439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.097 × 10⁹⁶(97-digit number)

10976285738196120463…70723304507792725441

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 410757

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 e09679d90b7856ff344f76e9c8f06a48345e914e53cd3d732aa066bf1b116e02

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 #410,757 on Chainz ↗