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Block #284,856

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/30/2013, 7:00:17 AM Β· Difficulty 9.9834 Β· 6,549,102 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ef5bd0bc9cb9ff26b79fee13f1d02e83a820d038789e9664ce04d9e4085f0585
View on Chainz β†—

Height

#284,856

Difficulty

9.983376

Transactions

1

Size

199 B

Version

2

Bits

09fbbe8e

Nonce

120,913

Timestamp

11/30/2013, 7:00:17 AM

Confirmations

6,549,102

Merkle Root

dbfb5967d31d26aede454bec4ce3c768a808e930890ce37488fcded5c7a92715
Transactions (1)
Coinbasedbfb5967d31d26…fcded5c7a92715
1 in β†’ 1 out10.0200 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.

3.374 Γ— 10⁹²(93-digit number)
33749868001189586427…94873548698407572480
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
3.374 Γ— 10⁹²(93-digit number)
33749868001189586427…94873548698407572479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.749 Γ— 10⁹²(93-digit number)
67499736002379172854…89747097396815144959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.349 Γ— 10⁹³(94-digit number)
13499947200475834570…79494194793630289919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.699 Γ— 10⁹³(94-digit number)
26999894400951669141…58988389587260579839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.399 Γ— 10⁹³(94-digit number)
53999788801903338283…17976779174521159679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.079 Γ— 10⁹⁴(95-digit number)
10799957760380667656…35953558349042319359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.159 Γ— 10⁹⁴(95-digit number)
21599915520761335313…71907116698084638719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.319 Γ— 10⁹⁴(95-digit number)
43199831041522670626…43814233396169277439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.639 Γ— 10⁹⁴(95-digit number)
86399662083045341253…87628466792338554879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.727 Γ— 10⁹⁡(96-digit number)
17279932416609068250…75256933584677109759
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 284856

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 ef5bd0bc9cb9ff26b79fee13f1d02e83a820d038789e9664ce04d9e4085f0585

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 #284,856 on Chainz β†—
Circulating Supply:57,915,892 XPMΒ·at block #6,833,957 Β· updates every 60s
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