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Block #307,970

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/12/2013, 8:54:58 PM Β· Difficulty 9.9944 Β· 6,518,198 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e1f013d72c2ecf4f98021320015192231c7cc43e01bc2147c55ecba3908b076f
View on Chainz β†—

Height

#307,970

Difficulty

9.994353

Transactions

1

Size

186 B

Version

2

Bits

09fe8ded

Nonce

4,881

Timestamp

12/12/2013, 8:54:58 PM

Confirmations

6,518,198

Merkle Root

966bb8752abda9cf1e4397608e02a65c2e8b0d8fafd9819ba95fdc68d157dde0
Transactions (1)
Coinbase966bb8752abda9…5fdc68d157dde0
1 in β†’ 1 out10.0000 XPM97 B
ANEZwy9t…E1uf5dKY
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.

1.339 Γ— 10⁹³(94-digit number)
13394973788298137202…55447834023942743360
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
1.339 Γ— 10⁹³(94-digit number)
13394973788298137202…55447834023942743359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.678 Γ— 10⁹³(94-digit number)
26789947576596274405…10895668047885486719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.357 Γ— 10⁹³(94-digit number)
53579895153192548811…21791336095770973439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.071 Γ— 10⁹⁴(95-digit number)
10715979030638509762…43582672191541946879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.143 Γ— 10⁹⁴(95-digit number)
21431958061277019524…87165344383083893759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.286 Γ— 10⁹⁴(95-digit number)
42863916122554039049…74330688766167787519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.572 Γ— 10⁹⁴(95-digit number)
85727832245108078098…48661377532335575039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.714 Γ— 10⁹⁡(96-digit number)
17145566449021615619…97322755064671150079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.429 Γ— 10⁹⁡(96-digit number)
34291132898043231239…94645510129342300159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.858 Γ— 10⁹⁡(96-digit number)
68582265796086462478…89291020258684600319
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 307970

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 e1f013d72c2ecf4f98021320015192231c7cc43e01bc2147c55ecba3908b076f

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 #307,970 on Chainz β†—
Circulating Supply:57,853,472 XPMΒ·at block #6,826,167 Β· updates every 60s
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