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Block #280,846

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/28/2013, 7:53:13 PM Β· Difficulty 9.9756 Β· 6,562,018 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
079885307abd6cd4e8783d732cd25d51731525cd702a53ac80b4d487b2c60da0
View on Chainz β†—

Height

#280,846

Difficulty

9.975597

Transactions

1

Size

208 B

Version

2

Bits

09f9c0bb

Nonce

3,244

Timestamp

11/28/2013, 7:53:13 PM

Confirmations

6,562,018

Merkle Root

cff9f574a634eacca9f9fef3db2aea73cad77951b2b31f566b75dec01ff89b44
Transactions (1)
Coinbasecff9f574a634ea…75dec01ff89b44
1 in β†’ 1 out10.0300 XPM116 B
AcLBm5Z9…S683d7c3
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.

4.877 Γ— 10⁹⁹(100-digit number)
48777948242279902023…50641978288525844480
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
4.877 Γ— 10⁹⁹(100-digit number)
48777948242279902023…50641978288525844479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.755 Γ— 10⁹⁹(100-digit number)
97555896484559804046…01283956577051688959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.951 Γ— 10¹⁰⁰(101-digit number)
19511179296911960809…02567913154103377919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.902 Γ— 10¹⁰⁰(101-digit number)
39022358593823921618…05135826308206755839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.804 Γ— 10¹⁰⁰(101-digit number)
78044717187647843237…10271652616413511679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.560 Γ— 10¹⁰¹(102-digit number)
15608943437529568647…20543305232827023359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.121 Γ— 10¹⁰¹(102-digit number)
31217886875059137295…41086610465654046719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.243 Γ— 10¹⁰¹(102-digit number)
62435773750118274590…82173220931308093439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.248 Γ— 10¹⁰²(103-digit number)
12487154750023654918…64346441862616186879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.497 Γ— 10¹⁰²(103-digit number)
24974309500047309836…28692883725232373759
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 280846

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 079885307abd6cd4e8783d732cd25d51731525cd702a53ac80b4d487b2c60da0

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 #280,846 on Chainz β†—
Circulating Supply:57,987,258 XPMΒ·at block #6,842,863 Β· updates every 60s
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