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Home/Chain Registry/Block #2,120,443

Block #2,120,443

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/17/2017, 9:32:49 AM Β· Difficulty 10.9118 Β· 4,680,051 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6abec061e864b6e8f56d895488a9f65c8d07d4fc2c2b93e00f98e39f069d5b37
View on Chainz β†—

Difficulty

10.911783

Transactions

1

Size

199 B

Version

2

Bits

0ae96a9f

Nonce

1,117,097,608

Timestamp

5/17/2017, 9:32:49 AM

Confirmations

4,680,051

Merkle Root

6689c9a85aa8532b55297328242bc3892a741a794b8abe56edb1720a2acd7680
Transactions (1)
Coinbase6689c9a85aa853…b1720a2acd7680
1 in β†’ 1 out8.3900 XPM109 B
Ac9orxxM…ikFZEHPe
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.

4.877 Γ— 10⁹⁴(95-digit number)
48772615459187104952…19043995375389710280
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
4.877 Γ— 10⁹⁴(95-digit number)
48772615459187104952…19043995375389710281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.754 Γ— 10⁹⁴(95-digit number)
97545230918374209904…38087990750779420561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.950 Γ— 10⁹⁡(96-digit number)
19509046183674841980…76175981501558841121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.901 Γ— 10⁹⁡(96-digit number)
39018092367349683961…52351963003117682241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.803 Γ— 10⁹⁡(96-digit number)
78036184734699367923…04703926006235364481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.560 Γ— 10⁹⁢(97-digit number)
15607236946939873584…09407852012470728961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.121 Γ— 10⁹⁢(97-digit number)
31214473893879747169…18815704024941457921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.242 Γ— 10⁹⁢(97-digit number)
62428947787759494338…37631408049882915841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.248 Γ— 10⁹⁷(98-digit number)
12485789557551898867…75262816099765831681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.497 Γ— 10⁹⁷(98-digit number)
24971579115103797735…50525632199531663361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.994 Γ— 10⁹⁷(98-digit number)
49943158230207595471…01051264399063326721
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 2120443

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 6abec061e864b6e8f56d895488a9f65c8d07d4fc2c2b93e00f98e39f069d5b37

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 #2,120,443 on Chainz β†—
Circulating Supply:57,648,014 XPMΒ·at block #6,800,493 Β· updates every 60s
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