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Block #351,572

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/9/2014, 7:06:51 PM Β· Difficulty 10.2975 Β· 6,447,260 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8b314b284221433ac996f985f765b8ff0d33fbde3848da11862a05182c140375
View on Chainz β†—

Height

#351,572

Difficulty

10.297489

Transactions

1

Size

206 B

Version

2

Bits

0a4c2845

Nonce

155,306

Timestamp

1/9/2014, 7:06:51 PM

Confirmations

6,447,260

Merkle Root

875a3e0499a70f9cebe18bd569700e6b2fa89ce90c6d9989ed22c95e057799cc
Transactions (1)
Coinbase875a3e0499a70f…22c95e057799cc
1 in β†’ 1 out9.4200 XPM116 B
AbwWkWZt…kawDhufa
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.

5.083 Γ— 10⁹³(94-digit number)
50838376036307903554…75849211521027705600
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
5.083 Γ— 10⁹³(94-digit number)
50838376036307903554…75849211521027705599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.016 Γ— 10⁹⁴(95-digit number)
10167675207261580710…51698423042055411199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.033 Γ— 10⁹⁴(95-digit number)
20335350414523161421…03396846084110822399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.067 Γ— 10⁹⁴(95-digit number)
40670700829046322843…06793692168221644799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.134 Γ— 10⁹⁴(95-digit number)
81341401658092645687…13587384336443289599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.626 Γ— 10⁹⁡(96-digit number)
16268280331618529137…27174768672886579199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.253 Γ— 10⁹⁡(96-digit number)
32536560663237058274…54349537345773158399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.507 Γ— 10⁹⁡(96-digit number)
65073121326474116549…08699074691546316799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.301 Γ— 10⁹⁢(97-digit number)
13014624265294823309…17398149383092633599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.602 Γ— 10⁹⁢(97-digit number)
26029248530589646619…34796298766185267199
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 351572

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 8b314b284221433ac996f985f765b8ff0d33fbde3848da11862a05182c140375

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 #351,572 on Chainz β†—
Circulating Supply:57,634,686 XPMΒ·at block #6,798,831 Β· updates every 60s
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