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Home/Chain Registry/Block #2,121,523

Block #2,121,523

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/18/2017, 1:51:43 AM Β· Difficulty 10.9136 Β· 4,710,424 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fa4244a828aa60968ef89cfc64770fe6560f2d46adc7cd267a2c45faf7e9dd4b
View on Chainz β†—

Difficulty

10.913571

Transactions

1

Size

199 B

Version

2

Bits

0ae9dfcc

Nonce

831,076,042

Timestamp

5/18/2017, 1:51:43 AM

Confirmations

4,710,424

Merkle Root

645f726b8281d225d69715039d61233bc8d7645f7a9954ad6a114b97691468aa
Transactions (1)
Coinbase645f726b8281d2…114b97691468aa
1 in β†’ 1 out8.3800 XPM109 B
AG4Je74X…7cvRzyLp
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.

5.459 Γ— 10⁹⁡(96-digit number)
54592675559570332519…90601189395581113600
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
5.459 Γ— 10⁹⁡(96-digit number)
54592675559570332519…90601189395581113599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.091 Γ— 10⁹⁢(97-digit number)
10918535111914066503…81202378791162227199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.183 Γ— 10⁹⁢(97-digit number)
21837070223828133007…62404757582324454399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.367 Γ— 10⁹⁢(97-digit number)
43674140447656266015…24809515164648908799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.734 Γ— 10⁹⁢(97-digit number)
87348280895312532031…49619030329297817599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.746 Γ— 10⁹⁷(98-digit number)
17469656179062506406…99238060658595635199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.493 Γ— 10⁹⁷(98-digit number)
34939312358125012812…98476121317191270399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.987 Γ— 10⁹⁷(98-digit number)
69878624716250025625…96952242634382540799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.397 Γ— 10⁹⁸(99-digit number)
13975724943250005125…93904485268765081599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.795 Γ— 10⁹⁸(99-digit number)
27951449886500010250…87808970537530163199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.590 Γ— 10⁹⁸(99-digit number)
55902899773000020500…75617941075060326399
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 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
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 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 2121523

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 fa4244a828aa60968ef89cfc64770fe6560f2d46adc7cd267a2c45faf7e9dd4b

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 #2,121,523 on Chainz β†—
Circulating Supply:57,899,696 XPMΒ·at block #6,831,946 Β· updates every 60s
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