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Block #60,270

2CCLength 8★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/18/2013, 7:02:14 AM · Difficulty 8.9685 · 6,729,674 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

c0f06475eb14043ee661e66cf6718756c55224f2735d4736d76f39d75b5f4878

View on Chainz ↗

Height

#60,270

Difficulty

8.968515

Transactions

Size

200 B

Version

Bits

08f7f09f

Nonce

209

Timestamp

7/18/2013, 7:02:14 AM

Confirmations

6,729,674

Merkle Root

d631c8b0166acf6faf6e21bc6d3c9e15fe723f72906352ff8701ffdc1c51d0d4

Transactions (1)

Coinbased631c8b0166acf…01ffdc1c51d0d4

1 in → 1 out12.4200 XPM110 B

AVKhrRMT…Bsdp3Qn7

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.

5.826 × 10⁹⁵(96-digit number)

58262526295309720297…87857102074771677470

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

5.826 × 10⁹⁵(96-digit number)

58262526295309720297…87857102074771677471

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.165 × 10⁹⁶(97-digit number)

11652505259061944059…75714204149543354941

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.330 × 10⁹⁶(97-digit number)

23305010518123888119…51428408299086709881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.661 × 10⁹⁶(97-digit number)

46610021036247776238…02856816598173419761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

9.322 × 10⁹⁶(97-digit number)

93220042072495552476…05713633196346839521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.864 × 10⁹⁷(98-digit number)

18644008414499110495…11427266392693679041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.728 × 10⁹⁷(98-digit number)

37288016828998220990…22854532785387358081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

7.457 × 10⁹⁷(98-digit number)

74576033657996441981…45709065570774716161

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 8 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

CommonChain length 8

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 60270

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 c0f06475eb14043ee661e66cf6718756c55224f2735d4736d76f39d75b5f4878

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 #60,270 on Chainz ↗