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Home/Chain Registry/Block #2,272,833

Block #2,272,833

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/29/2017, 4:18:22 AM Β· Difficulty 10.9543 Β· 4,571,263 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4c1126a480077aa49cd37a25089d13a40f8693b6e82dcb8f8a9bdb3ef32dde8f
View on Chainz β†—

Difficulty

10.954318

Transactions

1

Size

201 B

Version

2

Bits

0af44e35

Nonce

1,257,379,973

Timestamp

8/29/2017, 4:18:22 AM

Confirmations

4,571,263

Merkle Root

f52aedffe62c8539c27cbcb8dc6262d0bc6bd449c2d66b93fad1c86dc445d782
Transactions (1)
Coinbasef52aedffe62c85…d1c86dc445d782
1 in β†’ 1 out8.3200 XPM110 B
AYgApjUH…5K61Wbex
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.

4.832 Γ— 10⁹⁢(97-digit number)
48329846491718594408…83093324189589642240
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
4.832 Γ— 10⁹⁢(97-digit number)
48329846491718594408…83093324189589642241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.665 Γ— 10⁹⁢(97-digit number)
96659692983437188816…66186648379179284481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.933 Γ— 10⁹⁷(98-digit number)
19331938596687437763…32373296758358568961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.866 Γ— 10⁹⁷(98-digit number)
38663877193374875526…64746593516717137921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.732 Γ— 10⁹⁷(98-digit number)
77327754386749751053…29493187033434275841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.546 Γ— 10⁹⁸(99-digit number)
15465550877349950210…58986374066868551681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.093 Γ— 10⁹⁸(99-digit number)
30931101754699900421…17972748133737103361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.186 Γ— 10⁹⁸(99-digit number)
61862203509399800842…35945496267474206721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.237 Γ— 10⁹⁹(100-digit number)
12372440701879960168…71890992534948413441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.474 Γ— 10⁹⁹(100-digit number)
24744881403759920337…43781985069896826881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.948 Γ— 10⁹⁹(100-digit number)
49489762807519840674…87563970139793653761
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 2272833

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 4c1126a480077aa49cd37a25089d13a40f8693b6e82dcb8f8a9bdb3ef32dde8f

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 #2,272,833 on Chainz β†—
Circulating Supply:57,997,142 XPMΒ·at block #6,844,095 Β· updates every 60s
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