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Block #364,437

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/18/2014, 1:56:00 AM Β· Difficulty 10.4211 Β· 6,473,559 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bab9c5b91c6be34e4f75054998ddbe55f7fd5fed68dadb6103d94ec5db3eeb7e
View on Chainz β†—

Height

#364,437

Difficulty

10.421140

Transactions

1

Size

203 B

Version

2

Bits

0a6bcfd8

Nonce

108,994

Timestamp

1/18/2014, 1:56:00 AM

Confirmations

6,473,559

Merkle Root

ee97915f2a4265f4aa743ecc9675697f87d9e67f7b9f8682c75a76129bf86ee9
Transactions (1)
Coinbaseee97915f2a4265…5a76129bf86ee9
1 in β†’ 1 out9.1900 XPM110 B
AeKNrjNj…1NEq95Ta
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.

3.757 Γ— 10¹⁰²(103-digit number)
37579197410074531350…69400512376676819200
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
3.757 Γ— 10¹⁰²(103-digit number)
37579197410074531350…69400512376676819201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.515 Γ— 10¹⁰²(103-digit number)
75158394820149062700…38801024753353638401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.503 Γ— 10¹⁰³(104-digit number)
15031678964029812540…77602049506707276801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.006 Γ— 10¹⁰³(104-digit number)
30063357928059625080…55204099013414553601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.012 Γ— 10¹⁰³(104-digit number)
60126715856119250160…10408198026829107201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.202 Γ— 10¹⁰⁴(105-digit number)
12025343171223850032…20816396053658214401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.405 Γ— 10¹⁰⁴(105-digit number)
24050686342447700064…41632792107316428801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.810 Γ— 10¹⁰⁴(105-digit number)
48101372684895400128…83265584214632857601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.620 Γ— 10¹⁰⁴(105-digit number)
96202745369790800256…66531168429265715201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.924 Γ— 10¹⁰⁡(106-digit number)
19240549073958160051…33062336858531430401
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 364437

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 bab9c5b91c6be34e4f75054998ddbe55f7fd5fed68dadb6103d94ec5db3eeb7e

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 #364,437 on Chainz β†—
Circulating Supply:57,948,320 XPMΒ·at block #6,837,995 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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