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Block #149,122

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/4/2013, 4:14:51 AM Β· Difficulty 9.8566 Β· 6,677,660 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8dfdce6b387ab0aa92250b57203d8c7d6dd1c585f6477ccfb3f16b57f81067d5
View on Chainz β†—

Height

#149,122

Difficulty

9.856550

Transactions

1

Size

199 B

Version

2

Bits

09db46dd

Nonce

26,849

Timestamp

9/4/2013, 4:14:51 AM

Confirmations

6,677,660

Merkle Root

7d5ed74f6e4951ae9e70c1e1c8c38d15441bf7fe14797da6b00528398320a0b9
Transactions (1)
Coinbase7d5ed74f6e4951…0528398320a0b9
1 in β†’ 1 out10.2800 XPM109 B
AYKFccHZ…CdXZ542n
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.

7.020 Γ— 10⁹⁡(96-digit number)
70204744584179937407…19573446452855645120
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
7.020 Γ— 10⁹⁡(96-digit number)
70204744584179937407…19573446452855645119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.404 Γ— 10⁹⁢(97-digit number)
14040948916835987481…39146892905711290239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.808 Γ— 10⁹⁢(97-digit number)
28081897833671974962…78293785811422580479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.616 Γ— 10⁹⁢(97-digit number)
56163795667343949925…56587571622845160959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.123 Γ— 10⁹⁷(98-digit number)
11232759133468789985…13175143245690321919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.246 Γ— 10⁹⁷(98-digit number)
22465518266937579970…26350286491380643839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.493 Γ— 10⁹⁷(98-digit number)
44931036533875159940…52700572982761287679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.986 Γ— 10⁹⁷(98-digit number)
89862073067750319881…05401145965522575359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.797 Γ— 10⁹⁸(99-digit number)
17972414613550063976…10802291931045150719
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 149122

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 8dfdce6b387ab0aa92250b57203d8c7d6dd1c585f6477ccfb3f16b57f81067d5

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 #149,122 on Chainz β†—
Circulating Supply:57,858,417 XPMΒ·at block #6,826,781 Β· updates every 60s
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