Home/Chain Registry/Block #3,012,180

Block #3,012,180

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 1/16/2019, 3:25:02 PM · Difficulty 11.1785 · 3,829,658 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

c7f475f10dbfb606b343042ebb5a7ba8879f28143c6cc4d3583dcebe62ae05e9

View on Chainz ↗

Height

#3,012,180

Difficulty

11.178511

Transactions

Size

948 B

Version

Bits

0b2db2e7

Nonce

535,249,798

Timestamp

1/16/2019, 3:25:02 PM

Confirmations

3,829,658

Merkle Root

272ebf6bba6cde1ba3f6f049dcb431cf22fba162497141deb8a8c17a9396b6f7

Transactions (3)

Coinbase5cce9c59d6b626…cee8220cf6adea

1 in → 1 out8.0100 XPM109 B

AbXwmGxD…4XXYP765

0ff948b12f113f…64c933d7f2b0ca

2 in → 2 out7.5600 XPM374 B

AXgqVt4H…8rgyarso AUhjokok…k5m93PZR

0c0359cdcb6bf4…ec14835c5a9b36

2 in → 2 out7.4900 XPM375 B

AXh8UBXr…JUzAfddX AUhjokok…k5m93PZR

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.

5.777 × 10⁹⁴(95-digit number)

57770447095056339393…23872854837005315000

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

5.777 × 10⁹⁴(95-digit number)

57770447095056339393…23872854837005315001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.155 × 10⁹⁵(96-digit number)

11554089419011267878…47745709674010630001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.310 × 10⁹⁵(96-digit number)

23108178838022535757…95491419348021260001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.621 × 10⁹⁵(96-digit number)

46216357676045071514…90982838696042520001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

9.243 × 10⁹⁵(96-digit number)

92432715352090143029…81965677392085040001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.848 × 10⁹⁶(97-digit number)

18486543070418028605…63931354784170080001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.697 × 10⁹⁶(97-digit number)

36973086140836057211…27862709568340160001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

7.394 × 10⁹⁶(97-digit number)

73946172281672114423…55725419136680320001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.478 × 10⁹⁷(98-digit number)

14789234456334422884…11450838273360640001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.957 × 10⁹⁷(98-digit number)

29578468912668845769…22901676546721280001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

5.915 × 10⁹⁷(98-digit number)

59156937825337691538…45803353093442560001

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 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

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 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 3012180

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 c7f475f10dbfb606b343042ebb5a7ba8879f28143c6cc4d3583dcebe62ae05e9

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 #3,012,180 on Chainz ↗

Block #3,012,180

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