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Block #137,426

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/27/2013, 7:26:14 PM Β· Difficulty 9.8215 Β· 6,676,801 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
886eb1b05b37f3d73328b1a8b4d596649d5dd74201867b7724a0812aa9819b23
View on Chainz β†—

Height

#137,426

Difficulty

9.821454

Transactions

1

Size

203 B

Version

2

Bits

09d24ad1

Nonce

33,562,410

Timestamp

8/27/2013, 7:26:14 PM

Confirmations

6,676,801

Merkle Root

ed6f36f3baf5fc6198bcedf2a5daf652d3b26fbad6ee6af2ea6d9b9ddacd8d0a
Transactions (1)
Coinbaseed6f36f3baf5fc…6d9b9ddacd8d0a
1 in β†’ 1 out10.3500 XPM112 B
AT5A2KL6…CT16n6i2
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.

5.087 Γ— 10⁹⁷(98-digit number)
50871984275325819896…82742955372973820090
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
5.087 Γ— 10⁹⁷(98-digit number)
50871984275325819896…82742955372973820089
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.017 Γ— 10⁹⁸(99-digit number)
10174396855065163979…65485910745947640179
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.034 Γ— 10⁹⁸(99-digit number)
20348793710130327958…30971821491895280359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.069 Γ— 10⁹⁸(99-digit number)
40697587420260655917…61943642983790560719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.139 Γ— 10⁹⁸(99-digit number)
81395174840521311834…23887285967581121439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.627 Γ— 10⁹⁹(100-digit number)
16279034968104262366…47774571935162242879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.255 Γ— 10⁹⁹(100-digit number)
32558069936208524733…95549143870324485759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.511 Γ— 10⁹⁹(100-digit number)
65116139872417049467…91098287740648971519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.302 Γ— 10¹⁰⁰(101-digit number)
13023227974483409893…82196575481297943039
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 137426

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 886eb1b05b37f3d73328b1a8b4d596649d5dd74201867b7724a0812aa9819b23

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 #137,426 on Chainz β†—
Circulating Supply:57,757,886 XPMΒ·at block #6,814,226 Β· updates every 60s
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