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Block #135,771

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/26/2013, 8:02:14 PM Β· Difficulty 9.8123 Β· 6,682,220 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3d4adfd54e4cb87894bd12f361585b223cf82c95edbcbaee457f6eda7cb4d49b
View on Chainz β†—

Height

#135,771

Difficulty

9.812320

Transactions

2

Size

356 B

Version

2

Bits

09cff439

Nonce

123,433

Timestamp

8/26/2013, 8:02:14 PM

Confirmations

6,682,220

Merkle Root

d8e95c08e78844314906d0845dc775f150cc29334ad94b9c2200c83b112c498b
Transactions (2)
Coinbase971314c9dd2fef…21b4bce9bcb276
1 in β†’ 1 out10.3800 XPM109 B
AY88KHST…88L8yacq
81e85b94011eb2…14e6c70de0f75c
1 in β†’ 1 out10.4200 XPM158 B
AQj5CF31…Sfv2KzXY
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.

3.353 Γ— 10⁹²(93-digit number)
33532077566925634189…44025613221960050560
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
3.353 Γ— 10⁹²(93-digit number)
33532077566925634189…44025613221960050559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.706 Γ— 10⁹²(93-digit number)
67064155133851268379…88051226443920101119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.341 Γ— 10⁹³(94-digit number)
13412831026770253675…76102452887840202239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.682 Γ— 10⁹³(94-digit number)
26825662053540507351…52204905775680404479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.365 Γ— 10⁹³(94-digit number)
53651324107081014703…04409811551360808959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.073 Γ— 10⁹⁴(95-digit number)
10730264821416202940…08819623102721617919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.146 Γ— 10⁹⁴(95-digit number)
21460529642832405881…17639246205443235839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.292 Γ— 10⁹⁴(95-digit number)
42921059285664811762…35278492410886471679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.584 Γ— 10⁹⁴(95-digit number)
85842118571329623525…70556984821772943359
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 135771

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 3d4adfd54e4cb87894bd12f361585b223cf82c95edbcbaee457f6eda7cb4d49b

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 #135,771 on Chainz β†—
Circulating Supply:57,788,000 XPMΒ·at block #6,817,990 Β· updates every 60s
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