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Block #295,399

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/5/2013, 10:21:47 AM Β· Difficulty 9.9914 Β· 6,529,328 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6477f1c71caf90187b6fc3d0216dc360c2f9d11662ed641be990d7e4bc9cd6a2
View on Chainz β†—

Height

#295,399

Difficulty

9.991357

Transactions

1

Size

209 B

Version

2

Bits

09fdc999

Nonce

362,399

Timestamp

12/5/2013, 10:21:47 AM

Confirmations

6,529,328

Merkle Root

e4d17be1002e4a0ac13deddd5bd82a0321724d33b1a6ffb06c85ccac1362a13c
Transactions (1)
Coinbasee4d17be1002e4a…85ccac1362a13c
1 in β†’ 1 out10.0000 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.

2.371 Γ— 10¹⁰¹(102-digit number)
23711638220896805728…34172876923944213120
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
2.371 Γ— 10¹⁰¹(102-digit number)
23711638220896805728…34172876923944213119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.742 Γ— 10¹⁰¹(102-digit number)
47423276441793611456…68345753847888426239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.484 Γ— 10¹⁰¹(102-digit number)
94846552883587222912…36691507695776852479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.896 Γ— 10¹⁰²(103-digit number)
18969310576717444582…73383015391553704959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.793 Γ— 10¹⁰²(103-digit number)
37938621153434889164…46766030783107409919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.587 Γ— 10¹⁰²(103-digit number)
75877242306869778329…93532061566214819839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.517 Γ— 10¹⁰³(104-digit number)
15175448461373955665…87064123132429639679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.035 Γ— 10¹⁰³(104-digit number)
30350896922747911331…74128246264859279359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.070 Γ— 10¹⁰³(104-digit number)
60701793845495822663…48256492529718558719
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 295399

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 6477f1c71caf90187b6fc3d0216dc360c2f9d11662ed641be990d7e4bc9cd6a2

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 #295,399 on Chainz β†—
Circulating Supply:57,841,883 XPMΒ·at block #6,824,726 Β· updates every 60s
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