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Block #23,378

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/12/2013, 7:54:37 PM Β· Difficulty 7.9592 Β· 6,793,701 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
25da01148df90cb58d658b65ea1cb1d4504e7d90b0d757e4eb97e9b488c0ec2a
View on Chainz β†—

Height

#23,378

Difficulty

7.959175

Transactions

1

Size

199 B

Version

2

Bits

07f58c7b

Nonce

58

Timestamp

7/12/2013, 7:54:37 PM

Confirmations

6,793,701

Merkle Root

7b4fcbf23180f565c3bc213f0e8a71c1e888da940b524c77980c95385a25a531
Transactions (1)
Coinbase7b4fcbf23180f5…0c95385a25a531
1 in β†’ 1 out15.7600 XPM108 B
AdkCzGkh…5692zsoM
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.

9.239 Γ— 10⁹⁷(98-digit number)
92393711183015111970…35287332393326146920
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
9.239 Γ— 10⁹⁷(98-digit number)
92393711183015111970…35287332393326146919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.847 Γ— 10⁹⁸(99-digit number)
18478742236603022394…70574664786652293839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.695 Γ— 10⁹⁸(99-digit number)
36957484473206044788…41149329573304587679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.391 Γ— 10⁹⁸(99-digit number)
73914968946412089576…82298659146609175359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.478 Γ— 10⁹⁹(100-digit number)
14782993789282417915…64597318293218350719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.956 Γ— 10⁹⁹(100-digit number)
29565987578564835830…29194636586436701439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.913 Γ— 10⁹⁹(100-digit number)
59131975157129671661…58389273172873402879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.182 Γ— 10¹⁰⁰(101-digit number)
11826395031425934332…16778546345746805759
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8
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 23378

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 25da01148df90cb58d658b65ea1cb1d4504e7d90b0d757e4eb97e9b488c0ec2a

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 #23,378 on Chainz β†—
Circulating Supply:57,780,669 XPMΒ·at block #6,817,078 Β· updates every 60s
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