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Block #126,439

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/20/2013, 9:10:11 PM Β· Difficulty 9.7813 Β· 6,688,559 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f9da6ca5748feedfdf34d80bc18b7792f375074efb143cfda720688a2595fb7b
View on Chainz β†—

Height

#126,439

Difficulty

9.781291

Transactions

1

Size

204 B

Version

2

Bits

09c802b2

Nonce

671,300

Timestamp

8/20/2013, 9:10:11 PM

Confirmations

6,688,559

Merkle Root

2ad974a8dc121837efe96ba3cc79ee779e9f7c997aa328c9b80b3e7d34ef6505
Transactions (1)
Coinbase2ad974a8dc1218…0b3e7d34ef6505
1 in β†’ 1 out10.4400 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.

2.229 Γ— 10⁹⁸(99-digit number)
22292970160456734174…78388898646541730700
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
2.229 Γ— 10⁹⁸(99-digit number)
22292970160456734174…78388898646541730699
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.458 Γ— 10⁹⁸(99-digit number)
44585940320913468349…56777797293083461399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.917 Γ— 10⁹⁸(99-digit number)
89171880641826936698…13555594586166922799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.783 Γ— 10⁹⁹(100-digit number)
17834376128365387339…27111189172333845599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.566 Γ— 10⁹⁹(100-digit number)
35668752256730774679…54222378344667691199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.133 Γ— 10⁹⁹(100-digit number)
71337504513461549358…08444756689335382399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.426 Γ— 10¹⁰⁰(101-digit number)
14267500902692309871…16889513378670764799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.853 Γ— 10¹⁰⁰(101-digit number)
28535001805384619743…33779026757341529599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.707 Γ— 10¹⁰⁰(101-digit number)
57070003610769239487…67558053514683059199
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 126439

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 f9da6ca5748feedfdf34d80bc18b7792f375074efb143cfda720688a2595fb7b

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 #126,439 on Chainz β†—
Circulating Supply:57,764,071 XPMΒ·at block #6,814,997 Β· updates every 60s
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