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Home/Chain Registry/Block #2,114,370

Block #2,114,370

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/13/2017, 2:38:08 PM Β· Difficulty 10.9001 Β· 4,728,754 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
25bb1e38cf61d874d96e14acdda33b0377e52b39e5a7469388cbdb6c1d61eb46
View on Chainz β†—

Difficulty

10.900120

Transactions

2

Size

1.86 KB

Version

2

Bits

0ae66e3f

Nonce

240,095,088

Timestamp

5/13/2017, 2:38:08 PM

Confirmations

4,728,754

Merkle Root

3bc721924535c78a628c2d2c053d731411ceb107819fff753b2aedcffb445803
Transactions (2)
Coinbaseea8a0bd1ba24b9…83b975caf4bcc9
1 in β†’ 1 out8.4200 XPM109 B
AeM8CSHR…KPx4Cp3R
858c39a5177b67…a8689c1315c0d2
11 in β†’ 2 out40.2500 XPM1.67 KB
AaftQQdL…VsnTsiXYANy8XL34…aw5mrJYH
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.

1.804 Γ— 10⁹⁢(97-digit number)
18049893029736474637…99675887018280161280
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
1.804 Γ— 10⁹⁢(97-digit number)
18049893029736474637…99675887018280161281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.609 Γ— 10⁹⁢(97-digit number)
36099786059472949275…99351774036560322561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.219 Γ— 10⁹⁢(97-digit number)
72199572118945898550…98703548073120645121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.443 Γ— 10⁹⁷(98-digit number)
14439914423789179710…97407096146241290241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.887 Γ— 10⁹⁷(98-digit number)
28879828847578359420…94814192292482580481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.775 Γ— 10⁹⁷(98-digit number)
57759657695156718840…89628384584965160961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.155 Γ— 10⁹⁸(99-digit number)
11551931539031343768…79256769169930321921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.310 Γ— 10⁹⁸(99-digit number)
23103863078062687536…58513538339860643841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.620 Γ— 10⁹⁸(99-digit number)
46207726156125375072…17027076679721287681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.241 Γ— 10⁹⁸(99-digit number)
92415452312250750144…34054153359442575361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.848 Γ— 10⁹⁹(100-digit number)
18483090462450150028…68108306718885150721
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 2114370

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 25bb1e38cf61d874d96e14acdda33b0377e52b39e5a7469388cbdb6c1d61eb46

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 #2,114,370 on Chainz β†—
Circulating Supply:57,989,358 XPMΒ·at block #6,843,123 Β· updates every 60s
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