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Block #388,656

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/3/2014, 11:17:03 PM Β· Difficulty 10.4172 Β· 6,412,886 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a19bffd1d9e4dc222aef1cdfdbdb87163c8041f3bb513f3e286c2cb0b8cc9617
View on Chainz β†—

Height

#388,656

Difficulty

10.417197

Transactions

1

Size

202 B

Version

2

Bits

0a6acd71

Nonce

6,144

Timestamp

2/3/2014, 11:17:03 PM

Confirmations

6,412,886

Merkle Root

38b520f39b607cc2efb37a86a9d76de9fb1d878398e7a8a449030f68267898ae
Transactions (1)
Coinbase38b520f39b607c…030f68267898ae
1 in β†’ 1 out9.2000 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.

4.341 Γ— 10¹⁰⁰(101-digit number)
43415451070174052425…18844346055078694480
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
4.341 Γ— 10¹⁰⁰(101-digit number)
43415451070174052425…18844346055078694479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.683 Γ— 10¹⁰⁰(101-digit number)
86830902140348104850…37688692110157388959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.736 Γ— 10¹⁰¹(102-digit number)
17366180428069620970…75377384220314777919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.473 Γ— 10¹⁰¹(102-digit number)
34732360856139241940…50754768440629555839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.946 Γ— 10¹⁰¹(102-digit number)
69464721712278483880…01509536881259111679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.389 Γ— 10¹⁰²(103-digit number)
13892944342455696776…03019073762518223359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.778 Γ— 10¹⁰²(103-digit number)
27785888684911393552…06038147525036446719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.557 Γ— 10¹⁰²(103-digit number)
55571777369822787104…12076295050072893439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.111 Γ— 10¹⁰³(104-digit number)
11114355473964557420…24152590100145786879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.222 Γ— 10¹⁰³(104-digit number)
22228710947929114841…48305180200291573759
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 388656

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 a19bffd1d9e4dc222aef1cdfdbdb87163c8041f3bb513f3e286c2cb0b8cc9617

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 #388,656 on Chainz β†—
Circulating Supply:57,656,415 XPMΒ·at block #6,801,541 Β· updates every 60s
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