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Block #278,815

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/28/2013, 3:17:11 AM Β· Difficulty 9.9700 Β· 6,554,969 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
390b8f10588d0bc8ff164957462429e4fc9793b87abf627f0f6a7029f2f0e473
View on Chainz β†—

Height

#278,815

Difficulty

9.969963

Transactions

1

Size

201 B

Version

2

Bits

09f84f84

Nonce

46,424

Timestamp

11/28/2013, 3:17:11 AM

Confirmations

6,554,969

Merkle Root

f5717ced0e936cac2b55bfa649e9c2a25c8a0d5a7ea564150e5938bc70fbc990
Transactions (1)
Coinbasef5717ced0e936c…5938bc70fbc990
1 in β†’ 1 out10.0500 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.

1.438 Γ— 10⁹⁸(99-digit number)
14384040485712132513…65274606083569674240
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
1.438 Γ— 10⁹⁸(99-digit number)
14384040485712132513…65274606083569674239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.876 Γ— 10⁹⁸(99-digit number)
28768080971424265026…30549212167139348479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.753 Γ— 10⁹⁸(99-digit number)
57536161942848530052…61098424334278696959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.150 Γ— 10⁹⁹(100-digit number)
11507232388569706010…22196848668557393919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.301 Γ— 10⁹⁹(100-digit number)
23014464777139412020…44393697337114787839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.602 Γ— 10⁹⁹(100-digit number)
46028929554278824041…88787394674229575679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.205 Γ— 10⁹⁹(100-digit number)
92057859108557648083…77574789348459151359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.841 Γ— 10¹⁰⁰(101-digit number)
18411571821711529616…55149578696918302719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.682 Γ— 10¹⁰⁰(101-digit number)
36823143643423059233…10299157393836605439
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 278815

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 390b8f10588d0bc8ff164957462429e4fc9793b87abf627f0f6a7029f2f0e473

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 #278,815 on Chainz β†—
Circulating Supply:57,914,492 XPMΒ·at block #6,833,783 Β· updates every 60s
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