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Block #72,384

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/20/2013, 11:49:37 PM Β· Difficulty 8.9940 Β· 6,743,834 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
55bdf75861e6eeefdce9aac5d7c179e9598d58bc86365b63b2cae68be2d2be1e
View on Chainz β†—

Height

#72,384

Difficulty

8.994026

Transactions

1

Size

202 B

Version

2

Bits

08fe787a

Nonce

105

Timestamp

7/20/2013, 11:49:37 PM

Confirmations

6,743,834

Merkle Root

8bcdb39da5624c0657bd8b20da93b117e70745b03af1e43fc74ee69fa6ccb8a9
Transactions (1)
Coinbase8bcdb39da5624c…4ee69fa6ccb8a9
1 in β†’ 1 out12.3400 XPM110 B
AHGPtSCN…GESamBFW
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.

2.666 Γ— 10⁹⁸(99-digit number)
26668525756315364350…29823085162580516750
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
2.666 Γ— 10⁹⁸(99-digit number)
26668525756315364350…29823085162580516749
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.333 Γ— 10⁹⁸(99-digit number)
53337051512630728701…59646170325161033499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.066 Γ— 10⁹⁹(100-digit number)
10667410302526145740…19292340650322066999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.133 Γ— 10⁹⁹(100-digit number)
21334820605052291480…38584681300644133999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.266 Γ— 10⁹⁹(100-digit number)
42669641210104582960…77169362601288267999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.533 Γ— 10⁹⁹(100-digit number)
85339282420209165921…54338725202576535999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.706 Γ— 10¹⁰⁰(101-digit number)
17067856484041833184…08677450405153071999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.413 Γ— 10¹⁰⁰(101-digit number)
34135712968083666368…17354900810306143999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.827 Γ— 10¹⁰⁰(101-digit number)
68271425936167332737…34709801620612287999
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 72384

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 55bdf75861e6eeefdce9aac5d7c179e9598d58bc86365b63b2cae68be2d2be1e

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 #72,384 on Chainz β†—
Circulating Supply:57,773,873 XPMΒ·at block #6,816,217 Β· updates every 60s
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