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Block #461,445

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/26/2014, 5:46:36 PM Β· Difficulty 10.4151 Β· 6,369,109 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e0b083f63dc9dd9dae4f5c5897551df1e9eb23f15db18eaa3bd8929eac26cac7
View on Chainz β†—

Height

#461,445

Difficulty

10.415114

Transactions

1

Size

290 B

Version

2

Bits

0a6a44e7

Nonce

131,697

Timestamp

3/26/2014, 5:46:36 PM

Confirmations

6,369,109

Merkle Root

e68fdd44f3b0429b01012da269c9c224241711bb0de105dca7df5ea83c52cb7f
Transactions (1)
Coinbasee68fdd44f3b042…df5ea83c52cb7f
1 in β†’ 4 out9.2000 XPM199 B
AMVf7Jrg…xd5AVR7CALzzzbUz…2Cb4jSDNAa2Amg89…4rjYrsPZAJno7LX2…vo4wdWtY
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.

7.424 Γ— 10⁹⁢(97-digit number)
74242242466610145580…47918474006508016580
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
7.424 Γ— 10⁹⁢(97-digit number)
74242242466610145580…47918474006508016581
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.484 Γ— 10⁹⁷(98-digit number)
14848448493322029116…95836948013016033161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.969 Γ— 10⁹⁷(98-digit number)
29696896986644058232…91673896026032066321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.939 Γ— 10⁹⁷(98-digit number)
59393793973288116464…83347792052064132641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.187 Γ— 10⁹⁸(99-digit number)
11878758794657623292…66695584104128265281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.375 Γ— 10⁹⁸(99-digit number)
23757517589315246585…33391168208256530561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.751 Γ— 10⁹⁸(99-digit number)
47515035178630493171…66782336416513061121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.503 Γ— 10⁹⁸(99-digit number)
95030070357260986343…33564672833026122241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.900 Γ— 10⁹⁹(100-digit number)
19006014071452197268…67129345666052244481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.801 Γ— 10⁹⁹(100-digit number)
38012028142904394537…34258691332104488961
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 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
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 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 461445

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 e0b083f63dc9dd9dae4f5c5897551df1e9eb23f15db18eaa3bd8929eac26cac7

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 #461,445 on Chainz β†—
Circulating Supply:57,888,591 XPMΒ·at block #6,830,553 Β· updates every 60s
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