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Block #279,802

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/28/2013, 11:28:05 AM Β· Difficulty 9.9728 Β· 6,553,452 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
187f77b8ec08e0b487cc598a6e617db407707cb2646658c3df63c8c2e4139579
View on Chainz β†—

Height

#279,802

Difficulty

9.972806

Transactions

1

Size

1.04 KB

Version

2

Bits

09f909d6

Nonce

268,457

Timestamp

11/28/2013, 11:28:05 AM

Confirmations

6,553,452

Merkle Root

3db1075b84eed9ea1947295ed6a8dd634fb0eb1b5ab6e319be217a1747f3eee1
Transactions (1)
Coinbase3db1075b84eed9…217a1747f3eee1
1 in β†’ 27 out10.0400 XPM981 B
AN63YyQR…1tfe566AAScAzqGc…BZ6tV1vJAZ2pPuKg…95SN2Yr7AYrgZtF4…6oLCC7XKAQyr8Lw3…hs4nt3Pn
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.

7.631 Γ— 10⁹²(93-digit number)
76313293455524594765…53204789332667774720
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
7.631 Γ— 10⁹²(93-digit number)
76313293455524594765…53204789332667774719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.526 Γ— 10⁹³(94-digit number)
15262658691104918953…06409578665335549439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.052 Γ— 10⁹³(94-digit number)
30525317382209837906…12819157330671098879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.105 Γ— 10⁹³(94-digit number)
61050634764419675812…25638314661342197759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.221 Γ— 10⁹⁴(95-digit number)
12210126952883935162…51276629322684395519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.442 Γ— 10⁹⁴(95-digit number)
24420253905767870324…02553258645368791039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.884 Γ— 10⁹⁴(95-digit number)
48840507811535740649…05106517290737582079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.768 Γ— 10⁹⁴(95-digit number)
97681015623071481299…10213034581475164159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.953 Γ— 10⁹⁡(96-digit number)
19536203124614296259…20426069162950328319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.907 Γ— 10⁹⁡(96-digit number)
39072406249228592519…40852138325900656639
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 279802

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 187f77b8ec08e0b487cc598a6e617db407707cb2646658c3df63c8c2e4139579

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 #279,802 on Chainz β†—
Circulating Supply:57,910,223 XPMΒ·at block #6,833,253 Β· updates every 60s
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