Home/Chain Registry/Block #2,642,022

Block #2,642,022

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 5/1/2018, 1:58:15 PM · Difficulty 11.6397 · 4,190,913 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

f3c1559f2bbe781b6280c6e23f5eb22efb7e9537acf3b2baaec4424d60b31b3d

View on Chainz ↗

Height

#2,642,022

Difficulty

11.639733

Transactions

Size

878 B

Version

Bits

0ba3c58a

Nonce

401,665,990

Timestamp

5/1/2018, 1:58:15 PM

Confirmations

4,190,913

Merkle Root

81ba7dff2a4dbdb49cac7af4fe68ade5267240a96a03187c51b9ca7c796f9b5e

Transactions (4)

Coinbase37a64c0fffeb54…c021dc9766e78d

1 in → 1 out7.4000 XPM110 B

Adqah8zh…1WwoHJ9t

59ce73947c89ee…802571044059d3

1 in → 2 out295382.7387 XPM226 B

AJWF9PQf…XSuZaHJY AV7w2DGX…eTabtuuv

54029facc0588e…4dc84d17990ae9

1 in → 2 out293274.3237 XPM226 B

ATksYt2G…PcL67FV5 AYjaivKf…1HHdiRbZ

ee288dd0b6b9cb…f6658e519c28f0

1 in → 2 out293173.8585 XPM226 B

AXHiyfWY…YyCzCL9A ARJu8krJ…m6tCoLRj

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.

1.680 × 10⁹⁴(95-digit number)

16809073082343985242…55469016160044844640

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

1.680 × 10⁹⁴(95-digit number)

16809073082343985242…55469016160044844641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.361 × 10⁹⁴(95-digit number)

33618146164687970484…10938032320089689281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.723 × 10⁹⁴(95-digit number)

67236292329375940968…21876064640179378561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.344 × 10⁹⁵(96-digit number)

13447258465875188193…43752129280358757121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.689 × 10⁹⁵(96-digit number)

26894516931750376387…87504258560717514241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.378 × 10⁹⁵(96-digit number)

53789033863500752775…75008517121435028481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.075 × 10⁹⁶(97-digit number)

10757806772700150555…50017034242870056961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.151 × 10⁹⁶(97-digit number)

21515613545400301110…00034068485740113921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.303 × 10⁹⁶(97-digit number)

43031227090800602220…00068136971480227841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

8.606 × 10⁹⁶(97-digit number)

86062454181601204440…00136273942960455681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

1.721 × 10⁹⁷(98-digit number)

17212490836320240888…00272547885920911361

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 2642022

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 f3c1559f2bbe781b6280c6e23f5eb22efb7e9537acf3b2baaec4424d60b31b3d

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 #2,642,022 on Chainz ↗

Block #2,642,022

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