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Block #2,238,672

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/5/2017, 11:10:14 PM Β· Difficulty 10.9461 Β· 4,602,908 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
89d0c57ae76bd831a0510be751ce68e47aa8c5edf88bb470095e221c38832baf
View on Chainz β†—

Difficulty

10.946058

Transactions

1

Size

200 B

Version

2

Bits

0af230d5

Nonce

1,210,851,521

Timestamp

8/5/2017, 11:10:14 PM

Confirmations

4,602,908

Merkle Root

28d5fc27064566a4ec7b4f8ce7f48aa83cd65f8618077a46cbf49bf7bbb5d11d
Transactions (1)
Coinbase28d5fc27064566…f49bf7bbb5d11d
1 in β†’ 1 out8.3300 XPM110 B
AbLJK6r6…5GDpoicF
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.

6.255 Γ— 10⁹⁴(95-digit number)
62551150195726384376…81746675279460907360
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
6.255 Γ— 10⁹⁴(95-digit number)
62551150195726384376…81746675279460907359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.251 Γ— 10⁹⁡(96-digit number)
12510230039145276875…63493350558921814719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.502 Γ— 10⁹⁡(96-digit number)
25020460078290553750…26986701117843629439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.004 Γ— 10⁹⁡(96-digit number)
50040920156581107500…53973402235687258879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.000 Γ— 10⁹⁢(97-digit number)
10008184031316221500…07946804471374517759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.001 Γ— 10⁹⁢(97-digit number)
20016368062632443000…15893608942749035519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.003 Γ— 10⁹⁢(97-digit number)
40032736125264886000…31787217885498071039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.006 Γ— 10⁹⁢(97-digit number)
80065472250529772001…63574435770996142079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.601 Γ— 10⁹⁷(98-digit number)
16013094450105954400…27148871541992284159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.202 Γ— 10⁹⁷(98-digit number)
32026188900211908800…54297743083984568319
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 2238672

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 89d0c57ae76bd831a0510be751ce68e47aa8c5edf88bb470095e221c38832baf

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 #2,238,672 on Chainz β†—
Circulating Supply:57,977,026 XPMΒ·at block #6,841,579 Β· updates every 60s
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