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Block #288,642

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/1/2013, 8:22:51 PM Β· Difficulty 9.9879 Β· 6,522,989 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ec895a4dc44d6d59d640b01a2332692ad5511bb9cf94c811ec7d73266f3d633d
View on Chainz β†—

Height

#288,642

Difficulty

9.987866

Transactions

1

Size

200 B

Version

2

Bits

09fce4c9

Nonce

177,149

Timestamp

12/1/2013, 8:22:51 PM

Confirmations

6,522,989

Merkle Root

fa6b2ecb480cc10895de1f0df6b72b86a22f4ef7bc84b6b5fe53c80c05b20f1c
Transactions (1)
Coinbasefa6b2ecb480cc1…53c80c05b20f1c
1 in β†’ 1 out10.0100 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.

2.419 Γ— 10⁹⁴(95-digit number)
24194717678841460450…81314427076346670080
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
2.419 Γ— 10⁹⁴(95-digit number)
24194717678841460450…81314427076346670079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.838 Γ— 10⁹⁴(95-digit number)
48389435357682920901…62628854152693340159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.677 Γ— 10⁹⁴(95-digit number)
96778870715365841803…25257708305386680319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.935 Γ— 10⁹⁡(96-digit number)
19355774143073168360…50515416610773360639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.871 Γ— 10⁹⁡(96-digit number)
38711548286146336721…01030833221546721279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.742 Γ— 10⁹⁡(96-digit number)
77423096572292673442…02061666443093442559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.548 Γ— 10⁹⁢(97-digit number)
15484619314458534688…04123332886186885119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.096 Γ— 10⁹⁢(97-digit number)
30969238628917069377…08246665772373770239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.193 Γ— 10⁹⁢(97-digit number)
61938477257834138754…16493331544747540479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.238 Γ— 10⁹⁷(98-digit number)
12387695451566827750…32986663089495080959
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 288642

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 ec895a4dc44d6d59d640b01a2332692ad5511bb9cf94c811ec7d73266f3d633d

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 #288,642 on Chainz β†—
Circulating Supply:57,737,150 XPMΒ·at block #6,811,630 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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