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Home/Chain Registry/Block #2,434,119

Block #2,434,119

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/21/2017, 11:25:07 AM Β· Difficulty 10.9173 Β· 4,397,962 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8fae768534c8068937b02734e4652f5d4d52043a53aea3b693ee95970f6c3818
View on Chainz β†—

Difficulty

10.917329

Transactions

1

Size

198 B

Version

2

Bits

0aead615

Nonce

18,497,568

Timestamp

12/21/2017, 11:25:07 AM

Confirmations

4,397,962

Merkle Root

217cf3a1ad5e5f8cbf3711d0204c62c4a39cf84efda1f312018d4beb80c1afec
Transactions (1)
Coinbase217cf3a1ad5e5f…8d4beb80c1afec
1 in β†’ 1 out8.3800 XPM109 B
ALkWCPUP…SQMFAAUw
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.

6.374 Γ— 10⁹²(93-digit number)
63742044828436633176…48245223586746351040
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
6.374 Γ— 10⁹²(93-digit number)
63742044828436633176…48245223586746351039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.274 Γ— 10⁹³(94-digit number)
12748408965687326635…96490447173492702079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.549 Γ— 10⁹³(94-digit number)
25496817931374653270…92980894346985404159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.099 Γ— 10⁹³(94-digit number)
50993635862749306541…85961788693970808319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.019 Γ— 10⁹⁴(95-digit number)
10198727172549861308…71923577387941616639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.039 Γ— 10⁹⁴(95-digit number)
20397454345099722616…43847154775883233279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.079 Γ— 10⁹⁴(95-digit number)
40794908690199445233…87694309551766466559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.158 Γ— 10⁹⁴(95-digit number)
81589817380398890466…75388619103532933119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.631 Γ— 10⁹⁡(96-digit number)
16317963476079778093…50777238207065866239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.263 Γ— 10⁹⁡(96-digit number)
32635926952159556186…01554476414131732479
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2434119

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 8fae768534c8068937b02734e4652f5d4d52043a53aea3b693ee95970f6c3818

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 #2,434,119 on Chainz β†—
Circulating Supply:57,900,775 XPMΒ·at block #6,832,080 Β· updates every 60s
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