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Block #376,319

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/26/2014, 8:11:23 AM Β· Difficulty 10.4231 Β· 6,440,450 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7008c2b3c02e54ea6eca32eac4f22ecfb686e78e41e674ee38e2f2340d4a32ca
View on Chainz β†—

Height

#376,319

Difficulty

10.423128

Transactions

1

Size

206 B

Version

2

Bits

0a6c5218

Nonce

7,814

Timestamp

1/26/2014, 8:11:23 AM

Confirmations

6,440,450

Merkle Root

34349a28325398c6fc0430cff4b9a83bb50d56287d04676dbdc30b709c54d107
Transactions (1)
Coinbase34349a28325398…c30b709c54d107
1 in β†’ 1 out9.1900 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.

1.427 Γ— 10⁹⁡(96-digit number)
14277350030670455902…04046923811258696000
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
1.427 Γ— 10⁹⁡(96-digit number)
14277350030670455902…04046923811258695999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.855 Γ— 10⁹⁡(96-digit number)
28554700061340911805…08093847622517391999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.710 Γ— 10⁹⁡(96-digit number)
57109400122681823611…16187695245034783999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.142 Γ— 10⁹⁢(97-digit number)
11421880024536364722…32375390490069567999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.284 Γ— 10⁹⁢(97-digit number)
22843760049072729444…64750780980139135999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.568 Γ— 10⁹⁢(97-digit number)
45687520098145458889…29501561960278271999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.137 Γ— 10⁹⁢(97-digit number)
91375040196290917778…59003123920556543999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.827 Γ— 10⁹⁷(98-digit number)
18275008039258183555…18006247841113087999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.655 Γ— 10⁹⁷(98-digit number)
36550016078516367111…36012495682226175999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.310 Γ— 10⁹⁷(98-digit number)
73100032157032734222…72024991364452351999
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 376319

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 7008c2b3c02e54ea6eca32eac4f22ecfb686e78e41e674ee38e2f2340d4a32ca

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 #376,319 on Chainz β†—
Circulating Supply:57,778,185 XPMΒ·at block #6,816,768 Β· updates every 60s
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