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Home/Chain Registry/Block #2,226,121

Block #2,226,121

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/28/2017, 2:36:28 AM Β· Difficulty 10.9478 Β· 4,618,571 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
28cde0b9234cd26f1da3cf0285b0204550b42dca4f5b955cde87e61504ee1893
View on Chainz β†—

Difficulty

10.947826

Transactions

1

Size

199 B

Version

2

Bits

0af2a4bc

Nonce

574,302,061

Timestamp

7/28/2017, 2:36:28 AM

Confirmations

4,618,571

Merkle Root

e0fed06b7caa6dfdba6bce27bbd9ff34ddc05d020f344bed4200ff3f4d35f09d
Transactions (1)
Coinbasee0fed06b7caa6d…00ff3f4d35f09d
1 in β†’ 1 out8.3300 XPM109 B
ATgJGkhS…PSz31vSs
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.

5.709 Γ— 10⁹⁡(96-digit number)
57095628579184847909…20099476696361352960
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
5.709 Γ— 10⁹⁡(96-digit number)
57095628579184847909…20099476696361352959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.141 Γ— 10⁹⁢(97-digit number)
11419125715836969581…40198953392722705919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.283 Γ— 10⁹⁢(97-digit number)
22838251431673939163…80397906785445411839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.567 Γ— 10⁹⁢(97-digit number)
45676502863347878327…60795813570890823679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.135 Γ— 10⁹⁢(97-digit number)
91353005726695756654…21591627141781647359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.827 Γ— 10⁹⁷(98-digit number)
18270601145339151330…43183254283563294719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.654 Γ— 10⁹⁷(98-digit number)
36541202290678302661…86366508567126589439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.308 Γ— 10⁹⁷(98-digit number)
73082404581356605323…72733017134253178879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.461 Γ— 10⁹⁸(99-digit number)
14616480916271321064…45466034268506357759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.923 Γ— 10⁹⁸(99-digit number)
29232961832542642129…90932068537012715519
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 2226121

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 28cde0b9234cd26f1da3cf0285b0204550b42dca4f5b955cde87e61504ee1893

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 #2,226,121 on Chainz β†—
Circulating Supply:58,001,944 XPMΒ·at block #6,844,691 Β· updates every 60s
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