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Block #134,369

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/26/2013, 12:30:46 AM Β· Difficulty 9.8034 Β· 6,669,636 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
588b209f4ac28723628c0a15a4f1ba0eb60cbb34f338d94bc063e3461c081cfe
View on Chainz β†—

Height

#134,369

Difficulty

9.803445

Transactions

1

Size

198 B

Version

2

Bits

09cdae8b

Nonce

191,127

Timestamp

8/26/2013, 12:30:46 AM

Confirmations

6,669,636

Merkle Root

c353bd1a5f41657bf1eb10346bc534afd7f42a188150049f7a24be278b8cd866
Transactions (1)
Coinbasec353bd1a5f4165…24be278b8cd866
1 in β†’ 1 out10.3900 XPM109 B
AQAhV6Gm…zPsSKfi5
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.

1.533 Γ— 10⁹²(93-digit number)
15334599502613162566…32456329141280465920
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
1.533 Γ— 10⁹²(93-digit number)
15334599502613162566…32456329141280465919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.066 Γ— 10⁹²(93-digit number)
30669199005226325133…64912658282560931839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.133 Γ— 10⁹²(93-digit number)
61338398010452650266…29825316565121863679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.226 Γ— 10⁹³(94-digit number)
12267679602090530053…59650633130243727359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.453 Γ— 10⁹³(94-digit number)
24535359204181060106…19301266260487454719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.907 Γ— 10⁹³(94-digit number)
49070718408362120213…38602532520974909439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.814 Γ— 10⁹³(94-digit number)
98141436816724240426…77205065041949818879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.962 Γ— 10⁹⁴(95-digit number)
19628287363344848085…54410130083899637759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.925 Γ— 10⁹⁴(95-digit number)
39256574726689696170…08820260167799275519
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 134369

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 588b209f4ac28723628c0a15a4f1ba0eb60cbb34f338d94bc063e3461c081cfe

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 #134,369 on Chainz β†—
Circulating Supply:57,676,087 XPMΒ·at block #6,804,004 Β· updates every 60s
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