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Block #149,458

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/4/2013, 9:26:38 AM Β· Difficulty 9.8573 Β· 6,677,909 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d8b8ae4883204062ac978f37656dcf9274b3a4d6f85d9b3e06dc882613fb30dd
View on Chainz β†—

Height

#149,458

Difficulty

9.857262

Transactions

1

Size

199 B

Version

2

Bits

09db758d

Nonce

17,069

Timestamp

9/4/2013, 9:26:38 AM

Confirmations

6,677,909

Merkle Root

2c3c1f3289b06362abdc76540a5a9f03077a5cde9f770a21f625a8f8c4a65d90
Transactions (1)
Coinbase2c3c1f3289b063…25a8f8c4a65d90
1 in β†’ 1 out10.2800 XPM109 B
AbG35cX5…1ggEFgjQ
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.

3.846 Γ— 10⁹⁴(95-digit number)
38469678735560000199…54191159381035216000
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
3.846 Γ— 10⁹⁴(95-digit number)
38469678735560000199…54191159381035215999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.693 Γ— 10⁹⁴(95-digit number)
76939357471120000398…08382318762070431999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.538 Γ— 10⁹⁡(96-digit number)
15387871494224000079…16764637524140863999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.077 Γ— 10⁹⁡(96-digit number)
30775742988448000159…33529275048281727999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.155 Γ— 10⁹⁡(96-digit number)
61551485976896000318…67058550096563455999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.231 Γ— 10⁹⁢(97-digit number)
12310297195379200063…34117100193126911999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.462 Γ— 10⁹⁢(97-digit number)
24620594390758400127…68234200386253823999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.924 Γ— 10⁹⁢(97-digit number)
49241188781516800254…36468400772507647999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.848 Γ— 10⁹⁢(97-digit number)
98482377563033600509…72936801545015295999
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 149458

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 d8b8ae4883204062ac978f37656dcf9274b3a4d6f85d9b3e06dc882613fb30dd

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 #149,458 on Chainz β†—
Circulating Supply:57,863,037 XPMΒ·at block #6,827,366 Β· updates every 60s
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