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Block #726,336

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/17/2014, 8:42:22 PM Β· Difficulty 10.9610 Β· 6,079,862 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
eddd9d0a07c8dbf88f666f8a5ecd7ef211e2fbdb0f058b7c4a74ebefec85b638
View on Chainz β†—

Height

#726,336

Difficulty

10.960955

Transactions

1

Size

207 B

Version

2

Bits

0af60124

Nonce

1,754,630,552

Timestamp

9/17/2014, 8:42:22 PM

Confirmations

6,079,862

Merkle Root

3e7a027ae25f9fd551a6c5d0ca4a701a26659199158c3df8cc2912ab4037bcd5
Transactions (1)
Coinbase3e7a027ae25f9f…2912ab4037bcd5
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
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.

3.024 Γ— 10⁹⁢(97-digit number)
30241974284857981567…72918045117082347520
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
3.024 Γ— 10⁹⁢(97-digit number)
30241974284857981567…72918045117082347519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.048 Γ— 10⁹⁢(97-digit number)
60483948569715963134…45836090234164695039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.209 Γ— 10⁹⁷(98-digit number)
12096789713943192626…91672180468329390079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.419 Γ— 10⁹⁷(98-digit number)
24193579427886385253…83344360936658780159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.838 Γ— 10⁹⁷(98-digit number)
48387158855772770507…66688721873317560319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.677 Γ— 10⁹⁷(98-digit number)
96774317711545541014…33377443746635120639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.935 Γ— 10⁹⁸(99-digit number)
19354863542309108202…66754887493270241279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.870 Γ— 10⁹⁸(99-digit number)
38709727084618216405…33509774986540482559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.741 Γ— 10⁹⁸(99-digit number)
77419454169236432811…67019549973080965119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.548 Γ— 10⁹⁹(100-digit number)
15483890833847286562…34039099946161930239
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 726336

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 eddd9d0a07c8dbf88f666f8a5ecd7ef211e2fbdb0f058b7c4a74ebefec85b638

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 #726,336 on Chainz β†—
Circulating Supply:57,693,663 XPMΒ·at block #6,806,197 Β· updates every 60s
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