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Block #159,383

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/11/2013, 2:17:23 AM Β· Difficulty 9.8652 Β· 6,666,309 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
78780b4c4396a8609fff950e285602f660d9e658841c60df917188b7cfed668d
View on Chainz β†—

Height

#159,383

Difficulty

9.865223

Transactions

1

Size

197 B

Version

2

Bits

09dd7f39

Nonce

307,385

Timestamp

9/11/2013, 2:17:23 AM

Confirmations

6,666,309

Merkle Root

45396656396eb4212202e93c8d9da795619ebc847cf11d9d627056516889d280
Transactions (1)
Coinbase45396656396eb4…7056516889d280
1 in β†’ 1 out10.2600 XPM109 B
AP52EE3F…ZhqfNP3e
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.

1.816 Γ— 10⁹⁰(91-digit number)
18165028502078296184…24825563665378631000
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
1.816 Γ— 10⁹⁰(91-digit number)
18165028502078296184…24825563665378630999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.633 Γ— 10⁹⁰(91-digit number)
36330057004156592368…49651127330757261999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.266 Γ— 10⁹⁰(91-digit number)
72660114008313184737…99302254661514523999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.453 Γ— 10⁹¹(92-digit number)
14532022801662636947…98604509323029047999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.906 Γ— 10⁹¹(92-digit number)
29064045603325273895…97209018646058095999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.812 Γ— 10⁹¹(92-digit number)
58128091206650547790…94418037292116191999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.162 Γ— 10⁹²(93-digit number)
11625618241330109558…88836074584232383999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.325 Γ— 10⁹²(93-digit number)
23251236482660219116…77672149168464767999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.650 Γ— 10⁹²(93-digit number)
46502472965320438232…55344298336929535999
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 159383

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 78780b4c4396a8609fff950e285602f660d9e658841c60df917188b7cfed668d

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 #159,383 on Chainz β†—
Circulating Supply:57,849,647 XPMΒ·at block #6,825,691 Β· updates every 60s
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