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Block #1,432,550

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/28/2016, 9:26:25 AM · Difficulty 10.7869 · 5,409,743 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2ca8609c184d5327f96e4d811a9f60af360bc2cf3a69070f75eb0782fe580493

View on Chainz ↗

Height

#1,432,550

Difficulty

10.786876

Transactions

Size

809 B

Version

Bits

0ac970ae

Nonce

907,592,572

Timestamp

1/28/2016, 9:26:25 AM

Confirmations

5,409,743

Merkle Root

3be692f8cf3dab6c2c38c100ef0ed37de8a006aa8fa3f11840fe650dc66b2466

Transactions (4)

Coinbased71e1a347f9671…3f6ee1d6fa385c

1 in → 1 out8.6100 XPM110 B

AdebEV7c…wgwGfe7d

b748fa5896f7d4…8dc92157578b96

1 in → 2 out8.6400 XPM191 B

AYBwGriP…Y6HkoieN AXkFRrTx…1sa9PVWp

f76afa147d1f96…f9e666d7e323b0

1 in → 2 out8.6400 XPM192 B

AZLv6AqY…dt5jDYgp APuqXMwQ…NqPh6kEn

ec3af8fa762fa8…d6f8a59f3041e9

1 in → 2 out4.8600 XPM226 B

AXCz3i15…bd3tZodd AT4MskJ8…aDVPeq45

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.

9.743 × 10⁹⁵(96-digit number)

97431572359967928078…67849501334419901760

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

9.743 × 10⁹⁵(96-digit number)

97431572359967928078…67849501334419901759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.743 × 10⁹⁵(96-digit number)

97431572359967928078…67849501334419901761

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

1.948 × 10⁹⁶(97-digit number)

19486314471993585615…35699002668839803519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.948 × 10⁹⁶(97-digit number)

19486314471993585615…35699002668839803521

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

3.897 × 10⁹⁶(97-digit number)

38972628943987171231…71398005337679607039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.897 × 10⁹⁶(97-digit number)

38972628943987171231…71398005337679607041

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

7.794 × 10⁹⁶(97-digit number)

77945257887974342462…42796010675359214079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.794 × 10⁹⁶(97-digit number)

77945257887974342462…42796010675359214081

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

1.558 × 10⁹⁷(98-digit number)

15589051577594868492…85592021350718428159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.558 × 10⁹⁷(98-digit number)

15589051577594868492…85592021350718428161

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 1432550

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 2ca8609c184d5327f96e4d811a9f60af360bc2cf3a69070f75eb0782fe580493

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 #1,432,550 on Chainz ↗

Block #1,432,550

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