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Block #314,220

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/15/2013, 8:48:37 PM · Difficulty 10.0498 · 6,492,571 confirmations

2CC

Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header

Block Hash

119546992c077736df0e7c3a62df4e096debda97384477e65eed1176bd1f9ea7

View on Chainz ↗

Height

#314,220

Difficulty

10.049812

Transactions

Size

1.51 KB

Version

Bits

0a0cc073

Nonce

7,990

Timestamp

12/15/2013, 8:48:37 PM

Confirmations

6,492,571

Merkle Root

c86d94d697d6a83d707cabdc1d649df8ece14674bf2faedf19244965b2d7e6be

Transactions (4)

Coinbasea86ee8370a568b…2c0a4b2f720367

1 in → 21 out9.8900 XPM777 B

AYtDvcGs…VuAcA7m7 AbtgNzNb…9Atvu81w Aac9Hjdg…P4ktypc3 ANNg88pG…ppn21sTe Ad9pSzHt…cpJ3y2zz

2e44d1957ba170…36e259f6d172e6

1 in → 2 out9.9800 XPM226 B

AN7QU92Y…4oU9JhAV AGWqzgGV…5Gh2U1qK

feba2773c58c3c…a2b521b133e305

1 in → 2 out8.9419 XPM225 B

AUda7sSe…6pYCwqHZ AQskHSwo…neD2UP7e

26398fdd52e97a…41d6199918e1a9

1 in → 2 out8.9348 XPM225 B

AQnWMim4…qG8rjHWB AdYdXMC7…CVAmGUwd

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.

3.365 × 10⁹⁸(99-digit number)

33653354239546529452…70914382776405827600

Discovered Prime Numbers

p_k = 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.

origin + 1

3.365 × 10⁹⁸(99-digit number)

33653354239546529452…70914382776405827601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.730 × 10⁹⁸(99-digit number)

67306708479093058904…41828765552811655201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.346 × 10⁹⁹(100-digit number)

13461341695818611780…83657531105623310401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.692 × 10⁹⁹(100-digit number)

26922683391637223561…67315062211246620801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

5.384 × 10⁹⁹(100-digit number)

53845366783274447123…34630124422493241601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.076 × 10¹⁰⁰(101-digit number)

10769073356654889424…69260248844986483201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.153 × 10¹⁰⁰(101-digit number)

21538146713309778849…38520497689972966401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.307 × 10¹⁰⁰(101-digit number)

43076293426619557699…77040995379945932801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

8.615 × 10¹⁰⁰(101-digit number)

86152586853239115398…54081990759891865601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.723 × 10¹⁰¹(102-digit number)

17230517370647823079…08163981519783731201

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the Second Kind. 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 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 314220

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 119546992c077736df0e7c3a62df4e096debda97384477e65eed1176bd1f9ea7

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 #314,220 on Chainz ↗

Block #314,220

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