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Home/Chain Registry/Block #2,232,739

Block #2,232,739

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/1/2017, 8:01:25 PM Β· Difficulty 10.9461 Β· 4,612,007 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
158ca62708c10e067f9a1b22e92da3ee8452ea322089f93ebe1ff416690acb20
View on Chainz β†—

Difficulty

10.946053

Transactions

1

Size

200 B

Version

2

Bits

0af23084

Nonce

399,407,953

Timestamp

8/1/2017, 8:01:25 PM

Confirmations

4,612,007

Merkle Root

40814929b1a9005cd4a9b96053b8a8516310d68c1e9f39c5bbd1e54071357b29
Transactions (1)
Coinbase40814929b1a900…d1e54071357b29
1 in β†’ 1 out8.3300 XPM109 B
AdAVDBwV…wv8mKukD
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.

2.541 Γ— 10⁹⁢(97-digit number)
25410559740674204054…17993626903455736320
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
2.541 Γ— 10⁹⁢(97-digit number)
25410559740674204054…17993626903455736321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.082 Γ— 10⁹⁢(97-digit number)
50821119481348408108…35987253806911472641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.016 Γ— 10⁹⁷(98-digit number)
10164223896269681621…71974507613822945281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.032 Γ— 10⁹⁷(98-digit number)
20328447792539363243…43949015227645890561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.065 Γ— 10⁹⁷(98-digit number)
40656895585078726486…87898030455291781121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.131 Γ— 10⁹⁷(98-digit number)
81313791170157452973…75796060910583562241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.626 Γ— 10⁹⁸(99-digit number)
16262758234031490594…51592121821167124481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.252 Γ— 10⁹⁸(99-digit number)
32525516468062981189…03184243642334248961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.505 Γ— 10⁹⁸(99-digit number)
65051032936125962378…06368487284668497921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.301 Γ— 10⁹⁹(100-digit number)
13010206587225192475…12736974569336995841
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 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
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 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 2232739

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 158ca62708c10e067f9a1b22e92da3ee8452ea322089f93ebe1ff416690acb20

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 #2,232,739 on Chainz β†—
Circulating Supply:58,002,381 XPMΒ·at block #6,844,745 Β· updates every 60s
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