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Home/Chain Registry/Block #353,868

Block #353,868

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/11/2014, 4:57:20 AM Β· Difficulty 10.3342 Β· 6,458,748 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
776fc62df73d57e8976f61de443439f9aa6713adfe0368db59d5fb59d21c3963
View on Chainz β†—

Height

#353,868

Difficulty

10.334155

Transactions

1

Size

208 B

Version

2

Bits

0a558b35

Nonce

180,372

Timestamp

1/11/2014, 4:57:20 AM

Confirmations

6,458,748

Merkle Root

5c5ed84df1ee7eb7354c8beb8495e3e092b30800606a1808e01fc3d0db5633a1
Transactions (1)
Coinbase5c5ed84df1ee7e…1fc3d0db5633a1
1 in β†’ 1 out9.3500 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.

4.299 Γ— 10⁹⁸(99-digit number)
42997683308205733392…46627224129751029760
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
4.299 Γ— 10⁹⁸(99-digit number)
42997683308205733392…46627224129751029759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.599 Γ— 10⁹⁸(99-digit number)
85995366616411466784…93254448259502059519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.719 Γ— 10⁹⁹(100-digit number)
17199073323282293356…86508896519004119039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.439 Γ— 10⁹⁹(100-digit number)
34398146646564586713…73017793038008238079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.879 Γ— 10⁹⁹(100-digit number)
68796293293129173427…46035586076016476159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.375 Γ— 10¹⁰⁰(101-digit number)
13759258658625834685…92071172152032952319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.751 Γ— 10¹⁰⁰(101-digit number)
27518517317251669371…84142344304065904639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.503 Γ— 10¹⁰⁰(101-digit number)
55037034634503338742…68284688608131809279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.100 Γ— 10¹⁰¹(102-digit number)
11007406926900667748…36569377216263618559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.201 Γ— 10¹⁰¹(102-digit number)
22014813853801335496…73138754432527237119
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 353868

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 776fc62df73d57e8976f61de443439f9aa6713adfe0368db59d5fb59d21c3963

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 #353,868 on Chainz β†—
Circulating Supply:57,744,966 XPMΒ·at block #6,812,615 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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