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Block #74,609

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/21/2013, 12:02:15 PM Β· Difficulty 8.9956 Β· 6,727,262 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
fe3b3a63871ecb61c7b5669787a140422d80a0f668f7d79842df924db66aa19e
View on Chainz β†—

Height

#74,609

Difficulty

8.995620

Transactions

1

Size

201 B

Version

2

Bits

08fee0f3

Nonce

565

Timestamp

7/21/2013, 12:02:15 PM

Confirmations

6,727,262

Merkle Root

d061c00b30b8cd4f535e86dbdb497db758aeb8c74ae461ca32ecb2a5d8d2672e
Transactions (1)
Coinbased061c00b30b8cd…ecb2a5d8d2672e
1 in β†’ 1 out12.3400 XPM110 B
AeLhNtbC…dpMcpX5D
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.

1.432 Γ— 10⁹⁸(99-digit number)
14320540957860874413…33054703930600166720
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.432 Γ— 10⁹⁸(99-digit number)
14320540957860874413…33054703930600166721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.864 Γ— 10⁹⁸(99-digit number)
28641081915721748826…66109407861200333441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.728 Γ— 10⁹⁸(99-digit number)
57282163831443497652…32218815722400666881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.145 Γ— 10⁹⁹(100-digit number)
11456432766288699530…64437631444801333761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.291 Γ— 10⁹⁹(100-digit number)
22912865532577399061…28875262889602667521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.582 Γ— 10⁹⁹(100-digit number)
45825731065154798122…57750525779205335041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.165 Γ— 10⁹⁹(100-digit number)
91651462130309596244…15501051558410670081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.833 Γ— 10¹⁰⁰(101-digit number)
18330292426061919248…31002103116821340161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.666 Γ— 10¹⁰⁰(101-digit number)
36660584852123838497…62004206233642680321
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 74609

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 fe3b3a63871ecb61c7b5669787a140422d80a0f668f7d79842df924db66aa19e

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 #74,609 on Chainz β†—
Circulating Supply:57,659,061 XPMΒ·at block #6,801,870 Β· updates every 60s
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