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Block #131,754

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/24/2013, 12:08:40 PM Β· Difficulty 9.7858 Β· 6,694,415 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a7366676ee2bd8156ce964524a9d3471d6b998b5f9902c199871ace6bffc6b11
View on Chainz β†—

Height

#131,754

Difficulty

9.785759

Transactions

1

Size

201 B

Version

2

Bits

09c9277c

Nonce

201,372

Timestamp

8/24/2013, 12:08:40 PM

Confirmations

6,694,415

Merkle Root

50bc68d784cb86bdedf8c2398a38a5a8d3207f274c98ceedbb9636f3d584ea55
Transactions (1)
Coinbase50bc68d784cb86…9636f3d584ea55
1 in β†’ 1 out10.4300 XPM109 B
ANQwPCRX…Uw5XP32R
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.

4.051 Γ— 10⁹⁸(99-digit number)
40516325492794652124…54229178365700110320
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
4.051 Γ— 10⁹⁸(99-digit number)
40516325492794652124…54229178365700110319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.103 Γ— 10⁹⁸(99-digit number)
81032650985589304248…08458356731400220639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.620 Γ— 10⁹⁹(100-digit number)
16206530197117860849…16916713462800441279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.241 Γ— 10⁹⁹(100-digit number)
32413060394235721699…33833426925600882559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.482 Γ— 10⁹⁹(100-digit number)
64826120788471443398…67666853851201765119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.296 Γ— 10¹⁰⁰(101-digit number)
12965224157694288679…35333707702403530239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.593 Γ— 10¹⁰⁰(101-digit number)
25930448315388577359…70667415404807060479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.186 Γ— 10¹⁰⁰(101-digit number)
51860896630777154718…41334830809614120959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.037 Γ— 10¹⁰¹(102-digit number)
10372179326155430943…82669661619228241919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.074 Γ— 10¹⁰¹(102-digit number)
20744358652310861887…65339323238456483839
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 131754

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 a7366676ee2bd8156ce964524a9d3471d6b998b5f9902c199871ace6bffc6b11

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 #131,754 on Chainz β†—
Circulating Supply:57,853,480 XPMΒ·at block #6,826,168 Β· updates every 60s
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