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Home/Chain Registry/Block #2,650,591

Block #2,650,591

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/6/2018, 4:15:54 AM Β· Difficulty 11.7556 Β· 4,191,532 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cd667950c426d85ce7d265ba814467cc0b2e44d78bd9f2a44dde2b8a59e92968
View on Chainz β†—

Difficulty

11.755633

Transactions

1

Size

200 B

Version

2

Bits

0bc17132

Nonce

475,502,105

Timestamp

5/6/2018, 4:15:54 AM

Confirmations

4,191,532

Merkle Root

b2366ef4c3e17920dd1634623e0953cc525ae388eb64e02a2c1d2e7df4b20b9b
Transactions (1)
Coinbaseb2366ef4c3e179…1d2e7df4b20b9b
1 in β†’ 1 out7.2200 XPM110 B
AHi9kd3o…AP9tZM8o
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.047 Γ— 10⁹⁡(96-digit number)
10475131564173572455…30508433318382539000
Discovered Prime Numbers
p_k = 2^k Γ— 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.

1
origin + 1
1.047 Γ— 10⁹⁡(96-digit number)
10475131564173572455…30508433318382539001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.095 Γ— 10⁹⁡(96-digit number)
20950263128347144911…61016866636765078001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.190 Γ— 10⁹⁡(96-digit number)
41900526256694289822…22033733273530156001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.380 Γ— 10⁹⁡(96-digit number)
83801052513388579645…44067466547060312001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.676 Γ— 10⁹⁢(97-digit number)
16760210502677715929…88134933094120624001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.352 Γ— 10⁹⁢(97-digit number)
33520421005355431858…76269866188241248001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.704 Γ— 10⁹⁢(97-digit number)
67040842010710863716…52539732376482496001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.340 Γ— 10⁹⁷(98-digit number)
13408168402142172743…05079464752964992001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.681 Γ— 10⁹⁷(98-digit number)
26816336804284345486…10158929505929984001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.363 Γ— 10⁹⁷(98-digit number)
53632673608568690973…20317859011859968001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.072 Γ— 10⁹⁸(99-digit number)
10726534721713738194…40635718023719936001
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” 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 β†’
β˜…β˜…β˜…β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2650591

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 cd667950c426d85ce7d265ba814467cc0b2e44d78bd9f2a44dde2b8a59e92968

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 β†’ Debug Window β†’ 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 #2,650,591 on Chainz β†—
Circulating Supply:57,981,372 XPMΒ·at block #6,842,122 Β· updates every 60s
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