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.

3.204 × 10⁹⁴(95-digit number)

32043747120348512335…30392434990335753090

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

3.204 × 10⁹⁴(95-digit number)

32043747120348512335…30392434990335753089

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.204 × 10⁹⁴(95-digit number)

32043747120348512335…30392434990335753091

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

6.408 × 10⁹⁴(95-digit number)

64087494240697024670…60784869980671506179

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.408 × 10⁹⁴(95-digit number)

64087494240697024670…60784869980671506181

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

1.281 × 10⁹⁵(96-digit number)

12817498848139404934…21569739961343012359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.281 × 10⁹⁵(96-digit number)

12817498848139404934…21569739961343012361

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

2.563 × 10⁹⁵(96-digit number)

25634997696278809868…43139479922686024719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.563 × 10⁹⁵(96-digit number)

25634997696278809868…43139479922686024721

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

5.126 × 10⁹⁵(96-digit number)

51269995392557619736…86278959845372049439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.126 × 10⁹⁵(96-digit number)

51269995392557619736…86278959845372049441

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.025 × 10⁹⁶(97-digit number)

10253999078511523947…72557919690744098879

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

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 784107

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 4268adb50435a96355bc4608bdbd2afe347605ec5c27bad0c6c2e0dbaaee2508

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 #784,107 on Chainz ↗

Block #784,107

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