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Block #395,234

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/8/2014, 1:47:13 PM Β· Difficulty 10.4126 Β· 6,406,210 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a110203eff5a2f327fc14336bdcfefa7c47b090d6201db0e8bfd076c07a55d66
View on Chainz β†—

Height

#395,234

Difficulty

10.412641

Transactions

1

Size

210 B

Version

2

Bits

0a69a2d7

Nonce

1,696,901

Timestamp

2/8/2014, 1:47:13 PM

Confirmations

6,406,210

Merkle Root

160d3496b81a744c4decbc6f68b01c9def45f4e9a0116bdd818910c817eada35
Transactions (1)
Coinbase160d3496b81a74…8910c817eada35
1 in β†’ 1 out9.2100 XPM118 B
APS8BXgG…vuDwPaoc
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.

3.701 Γ— 10¹⁰⁰(101-digit number)
37015598875107168556…62270640396740198400
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
3.701 Γ— 10¹⁰⁰(101-digit number)
37015598875107168556…62270640396740198399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.403 Γ— 10¹⁰⁰(101-digit number)
74031197750214337112…24541280793480396799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.480 Γ— 10¹⁰¹(102-digit number)
14806239550042867422…49082561586960793599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.961 Γ— 10¹⁰¹(102-digit number)
29612479100085734844…98165123173921587199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.922 Γ— 10¹⁰¹(102-digit number)
59224958200171469689…96330246347843174399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.184 Γ— 10¹⁰²(103-digit number)
11844991640034293937…92660492695686348799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.368 Γ— 10¹⁰²(103-digit number)
23689983280068587875…85320985391372697599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.737 Γ— 10¹⁰²(103-digit number)
47379966560137175751…70641970782745395199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.475 Γ— 10¹⁰²(103-digit number)
94759933120274351503…41283941565490790399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.895 Γ— 10¹⁰³(104-digit number)
18951986624054870300…82567883130981580799
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 395234

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 a110203eff5a2f327fc14336bdcfefa7c47b090d6201db0e8bfd076c07a55d66

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 #395,234 on Chainz β†—
Circulating Supply:57,655,625 XPMΒ·at block #6,801,443 Β· updates every 60s
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