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Block #347,791

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/7/2014, 10:33:34 AM Β· Difficulty 10.2404 Β· 6,478,984 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0f2a076eeecd951e4689695b3ffc55deb711c7dd8b4abaa27b8bb7815bdc320c
View on Chainz β†—

Height

#347,791

Difficulty

10.240360

Transactions

1

Size

208 B

Version

2

Bits

0a3d883a

Nonce

139,873

Timestamp

1/7/2014, 10:33:34 AM

Confirmations

6,478,984

Merkle Root

8109fda5befad35dde11bebcd1f5e74385f61e529bd86aabf9d69a16fa26f9ad
Transactions (1)
Coinbase8109fda5befad3…d69a16fa26f9ad
1 in β†’ 1 out9.5200 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.

2.924 Γ— 10⁹⁸(99-digit number)
29245499173713033397…01219615262368624640
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
2.924 Γ— 10⁹⁸(99-digit number)
29245499173713033397…01219615262368624639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.849 Γ— 10⁹⁸(99-digit number)
58490998347426066795…02439230524737249279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.169 Γ— 10⁹⁹(100-digit number)
11698199669485213359…04878461049474498559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.339 Γ— 10⁹⁹(100-digit number)
23396399338970426718…09756922098948997119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.679 Γ— 10⁹⁹(100-digit number)
46792798677940853436…19513844197897994239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.358 Γ— 10⁹⁹(100-digit number)
93585597355881706873…39027688395795988479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.871 Γ— 10¹⁰⁰(101-digit number)
18717119471176341374…78055376791591976959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.743 Γ— 10¹⁰⁰(101-digit number)
37434238942352682749…56110753583183953919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.486 Γ— 10¹⁰⁰(101-digit number)
74868477884705365498…12221507166367907839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.497 Γ— 10¹⁰¹(102-digit number)
14973695576941073099…24443014332735815679
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 347791

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 0f2a076eeecd951e4689695b3ffc55deb711c7dd8b4abaa27b8bb7815bdc320c

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 #347,791 on Chainz β†—
Circulating Supply:57,858,360 XPMΒ·at block #6,826,774 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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