Home/Chain Registry/Block #2,650,960

Block #2,650,960

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 5/6/2018, 11:38:29 AM · Difficulty 11.7522 · 4,194,234 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

946aba5c255ffaefbb7727785ba021d87469adeeedf3653e7871e9dd90a3769c

View on Chainz ↗

Height

#2,650,960

Difficulty

11.752162

Transactions

Size

957 B

Version

Bits

0bc08db7

Nonce

307,825,244

Timestamp

5/6/2018, 11:38:29 AM

Confirmations

4,194,234

Merkle Root

ab0f19bd38df40391c74f31ec54dd8b793b3c9e414163973d7e88f4ff5e44800

Transactions (4)

Coinbase58247b26d17438…2c88bf6b30f624

1 in → 1 out7.2600 XPM110 B

Ac9cev3Z…256Xmx4T

c7e777213a3b76…e5d7282c1c1496

1 in → 2 out7.3800 XPM191 B

AJ1Hxuy3…yt2saQ3s AUkRFULb…4wHt2veo

318fbaadfcdb06…261796ee5beb9a

2 in → 2 out7.6961 XPM340 B

AM6XD26m…RcphfPC1 Aei5KPxA…2FzQLnLB

d37822f791da4f…185620023cc68a

1 in → 2 out6.2679 XPM225 B

AYnpgKTp…kDHJEMuE AHdTaHJi…RvnxAvYo

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.

8.685 × 10⁹⁶(97-digit number)

86856517576612615777…46500464013655040000

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

8.685 × 10⁹⁶(97-digit number)

86856517576612615777…46500464013655040001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.737 × 10⁹⁷(98-digit number)

17371303515322523155…93000928027310080001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.474 × 10⁹⁷(98-digit number)

34742607030645046310…86001856054620160001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

6.948 × 10⁹⁷(98-digit number)

69485214061290092621…72003712109240320001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.389 × 10⁹⁸(99-digit number)

13897042812258018524…44007424218480640001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.779 × 10⁹⁸(99-digit number)

27794085624516037048…88014848436961280001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

5.558 × 10⁹⁸(99-digit number)

55588171249032074097…76029696873922560001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.111 × 10⁹⁹(100-digit number)

11117634249806414819…52059393747845120001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.223 × 10⁹⁹(100-digit number)

22235268499612829638…04118787495690240001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

4.447 × 10⁹⁹(100-digit number)

44470536999225659277…08237574991380480001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

8.894 × 10⁹⁹(100-digit number)

88941073998451318555…16475149982760960001

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 2650960

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 946aba5c255ffaefbb7727785ba021d87469adeeedf3653e7871e9dd90a3769c

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 #2,650,960 on Chainz ↗

Block #2,650,960

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