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Block #169,732

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/18/2013, 6:12:21 AM Β· Difficulty 9.8666 Β· 6,671,672 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
df80b1becc95b9482d0951e1f39d193fd50fc24e3e49d51c08f0f3822313280b
View on Chainz β†—

Height

#169,732

Difficulty

9.866555

Transactions

1

Size

198 B

Version

2

Bits

09ddd687

Nonce

77,074

Timestamp

9/18/2013, 6:12:21 AM

Confirmations

6,671,672

Merkle Root

474860be5e0a720c7c6a5ddb34803e54bd26f8e17e63234cccbe257559d4f2ce
Transactions (1)
Coinbase474860be5e0a72…be257559d4f2ce
1 in β†’ 1 out10.2600 XPM109 B
AYAZW9za…da8AvwiQ
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.

1.504 Γ— 10⁹³(94-digit number)
15043216967584185298…56301521120283891840
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
1.504 Γ— 10⁹³(94-digit number)
15043216967584185298…56301521120283891839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.008 Γ— 10⁹³(94-digit number)
30086433935168370596…12603042240567783679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.017 Γ— 10⁹³(94-digit number)
60172867870336741192…25206084481135567359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.203 Γ— 10⁹⁴(95-digit number)
12034573574067348238…50412168962271134719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.406 Γ— 10⁹⁴(95-digit number)
24069147148134696476…00824337924542269439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.813 Γ— 10⁹⁴(95-digit number)
48138294296269392953…01648675849084538879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.627 Γ— 10⁹⁴(95-digit number)
96276588592538785907…03297351698169077759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.925 Γ— 10⁹⁡(96-digit number)
19255317718507757181…06594703396338155519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.851 Γ— 10⁹⁡(96-digit number)
38510635437015514363…13189406792676311039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.702 Γ— 10⁹⁡(96-digit number)
77021270874031028726…26378813585352622079
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 169732

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 df80b1becc95b9482d0951e1f39d193fd50fc24e3e49d51c08f0f3822313280b

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 #169,732 on Chainz β†—
Circulating Supply:57,975,606 XPMΒ·at block #6,841,403 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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