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Block #448,311

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/17/2014, 8:11:12 PM Β· Difficulty 10.3678 Β· 6,366,506 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a4100c0fd207bfb7a5e268ccca0c010dc0ef0b8c408fb97f526b27428a8695a3
View on Chainz β†—

Height

#448,311

Difficulty

10.367820

Transactions

1

Size

205 B

Version

2

Bits

0a5e296e

Nonce

42,039

Timestamp

3/17/2014, 8:11:12 PM

Confirmations

6,366,506

Merkle Root

e63d5b212a8b7374c06d9831c0f1dd3506b070f2454ad07add2110724a5a2120
Transactions (1)
Coinbasee63d5b212a8b73…2110724a5a2120
1 in β†’ 1 out9.2900 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.

5.482 Γ— 10¹⁰⁢(107-digit number)
54825828084095011787…10183573099281969280
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
5.482 Γ— 10¹⁰⁢(107-digit number)
54825828084095011787…10183573099281969279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.096 Γ— 10¹⁰⁷(108-digit number)
10965165616819002357…20367146198563938559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.193 Γ— 10¹⁰⁷(108-digit number)
21930331233638004714…40734292397127877119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.386 Γ— 10¹⁰⁷(108-digit number)
43860662467276009429…81468584794255754239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.772 Γ— 10¹⁰⁷(108-digit number)
87721324934552018859…62937169588511508479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.754 Γ— 10¹⁰⁸(109-digit number)
17544264986910403771…25874339177023016959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.508 Γ— 10¹⁰⁸(109-digit number)
35088529973820807543…51748678354046033919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.017 Γ— 10¹⁰⁸(109-digit number)
70177059947641615087…03497356708092067839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.403 Γ— 10¹⁰⁹(110-digit number)
14035411989528323017…06994713416184135679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.807 Γ— 10¹⁰⁹(110-digit number)
28070823979056646034…13989426832368271359
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 448311

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 a4100c0fd207bfb7a5e268ccca0c010dc0ef0b8c408fb97f526b27428a8695a3

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 #448,311 on Chainz β†—
Circulating Supply:57,762,623 XPMΒ·at block #6,814,816 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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