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Home/Chain Registry/Block #1,432,945

Block #1,432,945

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/28/2016, 2:11:52 PM Β· Difficulty 10.7915 Β· 5,411,900 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c375e77074603ca7774c1990b3205e2634683f98779d8db4c6b0c1ea5ec32e88
View on Chainz β†—

Difficulty

10.791468

Transactions

1

Size

200 B

Version

2

Bits

0aca9daa

Nonce

465,306,133

Timestamp

1/28/2016, 2:11:52 PM

Confirmations

5,411,900

Merkle Root

729e567dfcef529f3a7ef8893f2bf61d48dd98ac007529f93c1e59400fa3419c
Transactions (1)
Coinbase729e567dfcef52…1e59400fa3419c
1 in β†’ 1 out8.5700 XPM110 B
AUsYdLaB…88DUUWz8
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.

1.377 Γ— 10⁹⁡(96-digit number)
13774656599044297779…80886242185976281600
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
1.377 Γ— 10⁹⁡(96-digit number)
13774656599044297779…80886242185976281601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.754 Γ— 10⁹⁡(96-digit number)
27549313198088595559…61772484371952563201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.509 Γ— 10⁹⁡(96-digit number)
55098626396177191118…23544968743905126401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.101 Γ— 10⁹⁢(97-digit number)
11019725279235438223…47089937487810252801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.203 Γ— 10⁹⁢(97-digit number)
22039450558470876447…94179874975620505601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.407 Γ— 10⁹⁢(97-digit number)
44078901116941752894…88359749951241011201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.815 Γ— 10⁹⁢(97-digit number)
88157802233883505789…76719499902482022401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.763 Γ— 10⁹⁷(98-digit number)
17631560446776701157…53438999804964044801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.526 Γ— 10⁹⁷(98-digit number)
35263120893553402315…06877999609928089601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.052 Γ— 10⁹⁷(98-digit number)
70526241787106804631…13755999219856179201
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 1432945

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 c375e77074603ca7774c1990b3205e2634683f98779d8db4c6b0c1ea5ec32e88

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 #1,432,945 on Chainz β†—
Circulating Supply:58,003,170 XPMΒ·at block #6,844,844 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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