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Block #451,374

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/19/2014, 9:40:17 PM Β· Difficulty 10.3816 Β· 6,343,398 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
88b036c5177c4bbf2f5ba319b1c279a7727b0e1c1a3f5083b3fcc6e55c8dcdfd
View on Chainz β†—

Height

#451,374

Difficulty

10.381551

Transactions

1

Size

201 B

Version

2

Bits

0a61ad5b

Nonce

74,221

Timestamp

3/19/2014, 9:40:17 PM

Confirmations

6,343,398

Merkle Root

250652c738a14f33407065208b3f6697368603a64065925a18a2f4872cd9827e
Transactions (1)
Coinbase250652c738a14f…a2f4872cd9827e
1 in β†’ 1 out9.2600 XPM110 B
AeKNrjNj…1NEq95Ta
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.

1.460 Γ— 10⁹⁷(98-digit number)
14602011029275876251…74212581798818893120
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
1.460 Γ— 10⁹⁷(98-digit number)
14602011029275876251…74212581798818893119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.920 Γ— 10⁹⁷(98-digit number)
29204022058551752503…48425163597637786239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.840 Γ— 10⁹⁷(98-digit number)
58408044117103505007…96850327195275572479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.168 Γ— 10⁹⁸(99-digit number)
11681608823420701001…93700654390551144959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.336 Γ— 10⁹⁸(99-digit number)
23363217646841402003…87401308781102289919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.672 Γ— 10⁹⁸(99-digit number)
46726435293682804006…74802617562204579839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.345 Γ— 10⁹⁸(99-digit number)
93452870587365608012…49605235124409159679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.869 Γ— 10⁹⁹(100-digit number)
18690574117473121602…99210470248818319359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.738 Γ— 10⁹⁹(100-digit number)
37381148234946243204…98420940497636638719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.476 Γ— 10⁹⁹(100-digit number)
74762296469892486409…96841880995273277439
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 451374

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 88b036c5177c4bbf2f5ba319b1c279a7727b0e1c1a3f5083b3fcc6e55c8dcdfd

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 #451,374 on Chainz β†—
Circulating Supply:57,602,226 XPMΒ·at block #6,794,771 Β· updates every 60s
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