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Home/Chain Registry/Block #2,131,420

Block #2,131,420

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/25/2017, 2:23:38 AM Β· Difficulty 10.9101 Β· 4,710,778 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cbbfaccd2e4a18539eeb8c47ee768365e105debd3c86eb82c88ac7c0379f4b10
View on Chainz β†—

Difficulty

10.910142

Transactions

2

Size

426 B

Version

2

Bits

0ae8ff11

Nonce

1,872,604,744

Timestamp

5/25/2017, 2:23:38 AM

Confirmations

4,710,778

Merkle Root

09d9fa7cd456bcb0fd052dd444638e048d845adc05e60bc0a5cc186de41f80d0
Transactions (2)
Coinbase9bc8d18196f47a…c7d76d7ddf15da
1 in β†’ 1 out8.4000 XPM110 B
AWN44qSm…6NGHh634
312af9a857cc72…7de9ad2096e98c
1 in β†’ 2 out5765.3496 XPM226 B
APe7MFxP…LWenBVYtAJvxmec3…xoY5kW5s
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.

5.415 Γ— 10⁹³(94-digit number)
54153126256481992530…50665480238220279200
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
5.415 Γ— 10⁹³(94-digit number)
54153126256481992530…50665480238220279201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.083 Γ— 10⁹⁴(95-digit number)
10830625251296398506…01330960476440558401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.166 Γ— 10⁹⁴(95-digit number)
21661250502592797012…02661920952881116801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.332 Γ— 10⁹⁴(95-digit number)
43322501005185594024…05323841905762233601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.664 Γ— 10⁹⁴(95-digit number)
86645002010371188048…10647683811524467201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.732 Γ— 10⁹⁡(96-digit number)
17329000402074237609…21295367623048934401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.465 Γ— 10⁹⁡(96-digit number)
34658000804148475219…42590735246097868801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.931 Γ— 10⁹⁡(96-digit number)
69316001608296950438…85181470492195737601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.386 Γ— 10⁹⁢(97-digit number)
13863200321659390087…70362940984391475201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.772 Γ— 10⁹⁢(97-digit number)
27726400643318780175…40725881968782950401
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2131420

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 cbbfaccd2e4a18539eeb8c47ee768365e105debd3c86eb82c88ac7c0379f4b10

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 #2,131,420 on Chainz β†—
Circulating Supply:57,981,978 XPMΒ·at block #6,842,197 Β· updates every 60s
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