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Block #73,260

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/21/2013, 4:54:25 AM Β· Difficulty 8.9947 Β· 6,753,359 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dc2c05e350b6845a5b7f2d57ba20c21ed7e3eb2975e0689873c5b595193e3492
View on Chainz β†—

Height

#73,260

Difficulty

8.994692

Transactions

2

Size

719 B

Version

2

Bits

08fea422

Nonce

145

Timestamp

7/21/2013, 4:54:25 AM

Confirmations

6,753,359

Merkle Root

8f7cfbc6f5b5c4a644569a6dc8aa6689b4512873215f3d9af02599cc6d2bdddc
Transactions (2)
Coinbase4579a080dd7807…4e5841bfb60fca
1 in β†’ 1 out12.3500 XPM110 B
AMs7zhez…jgVgrR6Q
43ecc745f8c39b…24564aa67ed9ec
3 in β†’ 2 out532.0700 XPM521 B
AcqTroW1…S9Ypy8q7ALUVg4QQ…r3SnUqFN
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.

4.485 Γ— 10⁹⁰(91-digit number)
44859740630842387885…18143474825363789720
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
4.485 Γ— 10⁹⁰(91-digit number)
44859740630842387885…18143474825363789721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.971 Γ— 10⁹⁰(91-digit number)
89719481261684775770…36286949650727579441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.794 Γ— 10⁹¹(92-digit number)
17943896252336955154…72573899301455158881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.588 Γ— 10⁹¹(92-digit number)
35887792504673910308…45147798602910317761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.177 Γ— 10⁹¹(92-digit number)
71775585009347820616…90295597205820635521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.435 Γ— 10⁹²(93-digit number)
14355117001869564123…80591194411641271041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.871 Γ— 10⁹²(93-digit number)
28710234003739128246…61182388823282542081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.742 Γ— 10⁹²(93-digit number)
57420468007478256493…22364777646565084161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.148 Γ— 10⁹³(94-digit number)
11484093601495651298…44729555293130168321
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 73260

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 dc2c05e350b6845a5b7f2d57ba20c21ed7e3eb2975e0689873c5b595193e3492

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 #73,260 on Chainz β†—
Circulating Supply:57,857,105 XPMΒ·at block #6,826,618 Β· updates every 60s
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