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Block #461,678

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/26/2014, 9:36:27 PM Β· Difficulty 10.4154 Β· 6,363,775 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5e56b2a0ee298dc4540bec8d84fa27f8a6d9762d6b1a1c6f30785d53aaf93f0e
View on Chainz β†—

Height

#461,678

Difficulty

10.415369

Transactions

1

Size

193 B

Version

2

Bits

0a6a5599

Nonce

40,956

Timestamp

3/26/2014, 9:36:27 PM

Confirmations

6,363,775

Merkle Root

b0a23508df69112e85c5b2adf6e230d3015c981db1e033224f47860f538bc02a
Transactions (1)
Coinbaseb0a23508df6911…47860f538bc02a
1 in β†’ 1 out9.2000 XPM102 B
ASXb8Msj…BxGf64iZ
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.

2.164 Γ— 10⁹⁸(99-digit number)
21640988881502204140…90321651455160203480
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
2.164 Γ— 10⁹⁸(99-digit number)
21640988881502204140…90321651455160203479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.328 Γ— 10⁹⁸(99-digit number)
43281977763004408280…80643302910320406959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.656 Γ— 10⁹⁸(99-digit number)
86563955526008816560…61286605820640813919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.731 Γ— 10⁹⁹(100-digit number)
17312791105201763312…22573211641281627839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.462 Γ— 10⁹⁹(100-digit number)
34625582210403526624…45146423282563255679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.925 Γ— 10⁹⁹(100-digit number)
69251164420807053248…90292846565126511359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.385 Γ— 10¹⁰⁰(101-digit number)
13850232884161410649…80585693130253022719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.770 Γ— 10¹⁰⁰(101-digit number)
27700465768322821299…61171386260506045439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.540 Γ— 10¹⁰⁰(101-digit number)
55400931536645642599…22342772521012090879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.108 Γ— 10¹⁰¹(102-digit number)
11080186307329128519…44685545042024181759
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 461678

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 5e56b2a0ee298dc4540bec8d84fa27f8a6d9762d6b1a1c6f30785d53aaf93f0e

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 #461,678 on Chainz β†—
Circulating Supply:57,847,729 XPMΒ·at block #6,825,452 Β· updates every 60s
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