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Block #132,333

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/24/2013, 9:02:22 PM Β· Difficulty 9.7876 Β· 6,694,873 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4fcb310397fa5a297eabf21e013203ba6bd8e6b46337624e85587cd7964782d5
View on Chainz β†—

Height

#132,333

Difficulty

9.787627

Transactions

1

Size

198 B

Version

2

Bits

09c9a1e7

Nonce

12,904

Timestamp

8/24/2013, 9:02:22 PM

Confirmations

6,694,873

Merkle Root

3de6e66a3ce8f70121a9f655e52d6dd8817f4d191f314855422ba14ece03bb70
Transactions (1)
Coinbase3de6e66a3ce8f7…2ba14ece03bb70
1 in β†’ 1 out10.4200 XPM109 B
AWbAeqNJ…ox13tJA2
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.

1.913 Γ— 10⁹³(94-digit number)
19136411192283525013…77276950617511280780
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
1.913 Γ— 10⁹³(94-digit number)
19136411192283525013…77276950617511280779
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.827 Γ— 10⁹³(94-digit number)
38272822384567050027…54553901235022561559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.654 Γ— 10⁹³(94-digit number)
76545644769134100054…09107802470045123119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.530 Γ— 10⁹⁴(95-digit number)
15309128953826820010…18215604940090246239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.061 Γ— 10⁹⁴(95-digit number)
30618257907653640021…36431209880180492479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.123 Γ— 10⁹⁴(95-digit number)
61236515815307280043…72862419760360984959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.224 Γ— 10⁹⁡(96-digit number)
12247303163061456008…45724839520721969919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.449 Γ— 10⁹⁡(96-digit number)
24494606326122912017…91449679041443939839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.898 Γ— 10⁹⁡(96-digit number)
48989212652245824035…82899358082887879679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.797 Γ— 10⁹⁡(96-digit number)
97978425304491648070…65798716165775759359
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 132333

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 4fcb310397fa5a297eabf21e013203ba6bd8e6b46337624e85587cd7964782d5

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 #132,333 on Chainz β†—
Circulating Supply:57,861,746 XPMΒ·at block #6,827,205 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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