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Block #245,398

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/5/2013, 10:48:54 AM Β· Difficulty 9.9639 Β· 6,556,313 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f6ce06ea9ef5f5a64425502fc0edf0f072379b049906e9e19d25d7bbfe66d507
View on Chainz β†—

Height

#245,398

Difficulty

9.963876

Transactions

1

Size

207 B

Version

2

Bits

09f6c08d

Nonce

21,909

Timestamp

11/5/2013, 10:48:54 AM

Confirmations

6,556,313

Merkle Root

5bd042ea3081d6bc956c649149439edbe9bf598d9b3da55da00c55b0b47b203c
Transactions (1)
Coinbase5bd042ea3081d6…0c55b0b47b203c
1 in β†’ 1 out10.0600 XPM116 B
AcLBm5Z9…S683d7c3
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.

4.165 Γ— 10⁹⁷(98-digit number)
41653766330599918869…00800821517790060000
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
4.165 Γ— 10⁹⁷(98-digit number)
41653766330599918869…00800821517790059999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.330 Γ— 10⁹⁷(98-digit number)
83307532661199837738…01601643035580119999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.666 Γ— 10⁹⁸(99-digit number)
16661506532239967547…03203286071160239999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.332 Γ— 10⁹⁸(99-digit number)
33323013064479935095…06406572142320479999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.664 Γ— 10⁹⁸(99-digit number)
66646026128959870190…12813144284640959999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.332 Γ— 10⁹⁹(100-digit number)
13329205225791974038…25626288569281919999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.665 Γ— 10⁹⁹(100-digit number)
26658410451583948076…51252577138563839999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.331 Γ— 10⁹⁹(100-digit number)
53316820903167896152…02505154277127679999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.066 Γ— 10¹⁰⁰(101-digit number)
10663364180633579230…05010308554255359999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 245398

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 f6ce06ea9ef5f5a64425502fc0edf0f072379b049906e9e19d25d7bbfe66d507

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 #245,398 on Chainz β†—
Circulating Supply:57,657,780 XPMΒ·at block #6,801,710 Β· updates every 60s
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