Home/Chain Registry/Block #2,633,922

Block #2,633,922

2CCLength 12★★★★☆

Cunningham Chain of the Second Kind · Discovered 4/28/2018, 4:19:59 PM · Difficulty 11.2151 · 4,211,694 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

b142995240836590c32bcf1879ad48e9d931886df688408907db71717f2042a0

View on Chainz ↗

Height

#2,633,922

Difficulty

11.215146

Transactions

Size

939 B

Version

Bits

0b3713c8

Nonce

1,583,881,718

Timestamp

4/28/2018, 4:19:59 PM

Confirmations

4,211,694

Merkle Root

5c8de5969fa370f97008fdbaad57cc5006740f533391dbefa26228bb5d2247ba

Transactions (2)

Coinbase26b5f836409b73…5040d8ca3ba30f

1 in → 1 out7.9500 XPM110 B

AY1b3Ew7…QMLW3TUU

4fe891ec817f6e…9c57bf2246a81b

4 in → 4 out3014.3903 XPM739 B

ATogg1wq…ESc4sA8D AJsrgx7b…ggGpoV5j APGMxaLi…bhRD7nTc AepH8PP8…PJmCvLFP

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.

1.420 × 10⁹⁵(96-digit number)

14203047518959214657…16603549609594142720

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

1.420 × 10⁹⁵(96-digit number)

14203047518959214657…16603549609594142721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.840 × 10⁹⁵(96-digit number)

28406095037918429314…33207099219188285441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.681 × 10⁹⁵(96-digit number)

56812190075836858629…66414198438376570881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.136 × 10⁹⁶(97-digit number)

11362438015167371725…32828396876753141761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.272 × 10⁹⁶(97-digit number)

22724876030334743451…65656793753506283521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.544 × 10⁹⁶(97-digit number)

45449752060669486903…31313587507012567041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

9.089 × 10⁹⁶(97-digit number)

90899504121338973807…62627175014025134081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.817 × 10⁹⁷(98-digit number)

18179900824267794761…25254350028050268161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.635 × 10⁹⁷(98-digit number)

36359801648535589523…50508700056100536321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

7.271 × 10⁹⁷(98-digit number)

72719603297071179046…01017400112201072641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

1.454 × 10⁹⁸(99-digit number)

14543920659414235809…02034800224402145281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^11 × origin + 1

2.908 × 10⁹⁸(99-digit number)

29087841318828471618…04069600448804290561

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

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 2633922

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 b142995240836590c32bcf1879ad48e9d931886df688408907db71717f2042a0

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 #2,633,922 on Chainz ↗

Block #2,633,922

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