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Block #278,832

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/28/2013, 3:25:47 AM Β· Difficulty 9.9700 Β· 6,526,584 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2ed00e1d45a75473a6f8e251e1398d9de207f9a4135c6f7ca8cae9308e60fdd4
View on Chainz β†—

Height

#278,832

Difficulty

9.970013

Transactions

1

Size

199 B

Version

2

Bits

09f852c8

Nonce

49,690

Timestamp

11/28/2013, 3:25:47 AM

Confirmations

6,526,584

Merkle Root

454ce5d42dce1bc2f16efdde50ce7dc1e8920bfb53f66677ee20d4d1b5de85c8
Transactions (1)
Coinbase454ce5d42dce1b…20d4d1b5de85c8
1 in β†’ 1 out10.0500 XPM109 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.

7.876 Γ— 10⁹³(94-digit number)
78766501469461462955…13328042291749095200
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
7.876 Γ— 10⁹³(94-digit number)
78766501469461462955…13328042291749095199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.575 Γ— 10⁹⁴(95-digit number)
15753300293892292591…26656084583498190399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.150 Γ— 10⁹⁴(95-digit number)
31506600587784585182…53312169166996380799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.301 Γ— 10⁹⁴(95-digit number)
63013201175569170364…06624338333992761599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.260 Γ— 10⁹⁡(96-digit number)
12602640235113834072…13248676667985523199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.520 Γ— 10⁹⁡(96-digit number)
25205280470227668145…26497353335971046399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.041 Γ— 10⁹⁡(96-digit number)
50410560940455336291…52994706671942092799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.008 Γ— 10⁹⁢(97-digit number)
10082112188091067258…05989413343884185599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.016 Γ— 10⁹⁢(97-digit number)
20164224376182134516…11978826687768371199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.032 Γ— 10⁹⁢(97-digit number)
40328448752364269033…23957653375536742399
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 278832

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 2ed00e1d45a75473a6f8e251e1398d9de207f9a4135c6f7ca8cae9308e60fdd4

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 #278,832 on Chainz β†—
Circulating Supply:57,687,399 XPMΒ·at block #6,805,415 Β· updates every 60s
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