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Block #307,594

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/12/2013, 4:20:21 PM Β· Difficulty 9.9942 Β· 6,518,512 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
946c8ad24863ddd94ba15c2bfe3a315a175497184a34bc58cbc6246809e43bd4
View on Chainz β†—

Height

#307,594

Difficulty

9.994226

Transactions

2

Size

357 B

Version

2

Bits

09fe859b

Nonce

32,983

Timestamp

12/12/2013, 4:20:21 PM

Confirmations

6,518,512

Merkle Root

facb92f55a88c3004188f533c9716b47a117db37403c2da061bc98fb2a5219d2
Transactions (2)
Coinbase9273e1eec44835…5f7ed0df1af14b
1 in β†’ 1 out10.0100 XPM109 B
AeKNrjNj…1NEq95Ta
3b90936b7930cb…b4632094760df8
1 in β†’ 1 out10.0200 XPM157 B
ANF2bpUH…8Z1WQvCv
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.

7.535 Γ— 10⁹⁡(96-digit number)
75356559886894661883…90038970724259947520
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
7.535 Γ— 10⁹⁡(96-digit number)
75356559886894661883…90038970724259947519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.507 Γ— 10⁹⁢(97-digit number)
15071311977378932376…80077941448519895039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.014 Γ— 10⁹⁢(97-digit number)
30142623954757864753…60155882897039790079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.028 Γ— 10⁹⁢(97-digit number)
60285247909515729506…20311765794079580159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.205 Γ— 10⁹⁷(98-digit number)
12057049581903145901…40623531588159160319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.411 Γ— 10⁹⁷(98-digit number)
24114099163806291802…81247063176318320639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.822 Γ— 10⁹⁷(98-digit number)
48228198327612583605…62494126352636641279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.645 Γ— 10⁹⁷(98-digit number)
96456396655225167210…24988252705273282559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.929 Γ— 10⁹⁸(99-digit number)
19291279331045033442…49976505410546565119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.858 Γ— 10⁹⁸(99-digit number)
38582558662090066884…99953010821093130239
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 307594

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 946c8ad24863ddd94ba15c2bfe3a315a175497184a34bc58cbc6246809e43bd4

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 #307,594 on Chainz β†—
Circulating Supply:57,852,971 XPMΒ·at block #6,826,105 Β· updates every 60s
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