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Block #311,683

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/14/2013, 4:27:44 PM Β· Difficulty 9.9956 Β· 6,484,812 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f040cf74a95e41ab2e7b72401258a9965d4325e7c2bfed81021966dfd26d4762
View on Chainz β†—

Height

#311,683

Difficulty

9.995564

Transactions

1

Size

210 B

Version

2

Bits

09fedd4f

Nonce

268,436,152

Timestamp

12/14/2013, 4:27:44 PM

Confirmations

6,484,812

Merkle Root

568ae7e4d0ba1cf6668955fc097c084ec7b652ce1f4f01da75e15e4e67fe784b
Transactions (1)
Coinbase568ae7e4d0ba1c…e15e4e67fe784b
1 in β†’ 1 out9.9900 XPM116 B
AbwWkWZt…kawDhufa
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.

6.051 Γ— 10¹⁰³(104-digit number)
60512478134172787034…88015349973927436080
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
6.051 Γ— 10¹⁰³(104-digit number)
60512478134172787034…88015349973927436079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.210 Γ— 10¹⁰⁴(105-digit number)
12102495626834557406…76030699947854872159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.420 Γ— 10¹⁰⁴(105-digit number)
24204991253669114813…52061399895709744319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.840 Γ— 10¹⁰⁴(105-digit number)
48409982507338229627…04122799791419488639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.681 Γ— 10¹⁰⁴(105-digit number)
96819965014676459255…08245599582838977279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.936 Γ— 10¹⁰⁡(106-digit number)
19363993002935291851…16491199165677954559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.872 Γ— 10¹⁰⁡(106-digit number)
38727986005870583702…32982398331355909119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.745 Γ— 10¹⁰⁡(106-digit number)
77455972011741167404…65964796662711818239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.549 Γ— 10¹⁰⁢(107-digit number)
15491194402348233480…31929593325423636479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.098 Γ— 10¹⁰⁢(107-digit number)
30982388804696466961…63859186650847272959
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 311683

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 f040cf74a95e41ab2e7b72401258a9965d4325e7c2bfed81021966dfd26d4762

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 #311,683 on Chainz β†—
Circulating Supply:57,615,960 XPMΒ·at block #6,796,494 Β· updates every 60s
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