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Block #375,056

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/25/2014, 11:25:35 AM Β· Difficulty 10.4209 Β· 6,425,424 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
030d78a0f6eef78b0cb3b86afe85d9b9ff82a32395099ea9ab3761ab399bfe23
View on Chainz β†—

Height

#375,056

Difficulty

10.420874

Transactions

1

Size

198 B

Version

2

Bits

0a6bbe6d

Nonce

41,217

Timestamp

1/25/2014, 11:25:35 AM

Confirmations

6,425,424

Merkle Root

b3102641109ea7bd4532cdac91e4bd8994fd48d4b104cbe2e8deeeb321eaa511
Transactions (1)
Coinbaseb3102641109ea7…deeeb321eaa511
1 in β†’ 1 out9.1900 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.

5.729 Γ— 10⁸⁹(90-digit number)
57291335622839024869…08090477791468182800
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
5.729 Γ— 10⁸⁹(90-digit number)
57291335622839024869…08090477791468182799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.145 Γ— 10⁹⁰(91-digit number)
11458267124567804973…16180955582936365599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.291 Γ— 10⁹⁰(91-digit number)
22916534249135609947…32361911165872731199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.583 Γ— 10⁹⁰(91-digit number)
45833068498271219895…64723822331745462399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.166 Γ— 10⁹⁰(91-digit number)
91666136996542439791…29447644663490924799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.833 Γ— 10⁹¹(92-digit number)
18333227399308487958…58895289326981849599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.666 Γ— 10⁹¹(92-digit number)
36666454798616975916…17790578653963699199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.333 Γ— 10⁹¹(92-digit number)
73332909597233951833…35581157307927398399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.466 Γ— 10⁹²(93-digit number)
14666581919446790366…71162314615854796799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.933 Γ— 10⁹²(93-digit number)
29333163838893580733…42324629231709593599
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 375056

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 030d78a0f6eef78b0cb3b86afe85d9b9ff82a32395099ea9ab3761ab399bfe23

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 #375,056 on Chainz β†—
Circulating Supply:57,647,901 XPMΒ·at block #6,800,479 Β· updates every 60s
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