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Block #269,393

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/23/2013, 2:30:03 AM Β· Difficulty 9.9534 Β· 6,555,285 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
bdf0eba873f2a7aac2421bd5422ef82811649b63cd7ffdf4040e42efba1dd408
View on Chainz β†—

Height

#269,393

Difficulty

9.953378

Transactions

1

Size

198 B

Version

2

Bits

09f41097

Nonce

144,678

Timestamp

11/23/2013, 2:30:03 AM

Confirmations

6,555,285

Merkle Root

34e8869680375e4a4880c59ca4d30975e061a5f8c3a784caf11dd976bb1a168a
Transactions (1)
Coinbase34e8869680375e…1dd976bb1a168a
1 in β†’ 1 out10.0800 XPM109 B
AR1c6GU1…zzkggCDv
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.

1.865 Γ— 10⁹³(94-digit number)
18651886752298710478…74045124152846868480
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
1.865 Γ— 10⁹³(94-digit number)
18651886752298710478…74045124152846868479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.730 Γ— 10⁹³(94-digit number)
37303773504597420956…48090248305693736959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.460 Γ— 10⁹³(94-digit number)
74607547009194841913…96180496611387473919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.492 Γ— 10⁹⁴(95-digit number)
14921509401838968382…92360993222774947839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.984 Γ— 10⁹⁴(95-digit number)
29843018803677936765…84721986445549895679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.968 Γ— 10⁹⁴(95-digit number)
59686037607355873531…69443972891099791359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.193 Γ— 10⁹⁡(96-digit number)
11937207521471174706…38887945782199582719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.387 Γ— 10⁹⁡(96-digit number)
23874415042942349412…77775891564399165439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.774 Γ— 10⁹⁡(96-digit number)
47748830085884698824…55551783128798330879
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 269393

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 bdf0eba873f2a7aac2421bd5422ef82811649b63cd7ffdf4040e42efba1dd408

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 #269,393 on Chainz β†—
Circulating Supply:57,841,488 XPMΒ·at block #6,824,677 Β· updates every 60s
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