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Block #149,611

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/4/2013, 12:02:50 PM Β· Difficulty 9.8572 Β· 6,646,151 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d307ce4dff0035cabbfc2c601e3938c2cdb3d14b40b648421f0ffe13b2dc48e5
View on Chainz β†—

Height

#149,611

Difficulty

9.857179

Transactions

1

Size

199 B

Version

2

Bits

09db7019

Nonce

10,673

Timestamp

9/4/2013, 12:02:50 PM

Confirmations

6,646,151

Merkle Root

f68d82c8a86babe8b8f6f4b1d92979d3a8a9e37dc5998a9973fdbdbe4fbffcab
Transactions (1)
Coinbasef68d82c8a86bab…fdbdbe4fbffcab
1 in β†’ 1 out10.2800 XPM109 B
AP9bALPc…xk8hhiNs
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.

7.035 Γ— 10⁹⁴(95-digit number)
70350439473326661368…63190738188736514650
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
7.035 Γ— 10⁹⁴(95-digit number)
70350439473326661368…63190738188736514649
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.407 Γ— 10⁹⁡(96-digit number)
14070087894665332273…26381476377473029299
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.814 Γ— 10⁹⁡(96-digit number)
28140175789330664547…52762952754946058599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.628 Γ— 10⁹⁡(96-digit number)
56280351578661329094…05525905509892117199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.125 Γ— 10⁹⁢(97-digit number)
11256070315732265818…11051811019784234399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.251 Γ— 10⁹⁢(97-digit number)
22512140631464531637…22103622039568468799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.502 Γ— 10⁹⁢(97-digit number)
45024281262929063275…44207244079136937599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.004 Γ— 10⁹⁢(97-digit number)
90048562525858126551…88414488158273875199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.800 Γ— 10⁹⁷(98-digit number)
18009712505171625310…76828976316547750399
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 149611

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 d307ce4dff0035cabbfc2c601e3938c2cdb3d14b40b648421f0ffe13b2dc48e5

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 #149,611 on Chainz β†—
Circulating Supply:57,610,177 XPMΒ·at block #6,795,761 Β· updates every 60s
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