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Block #59,164

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/18/2013, 12:40:37 AM Β· Difficulty 8.9636 Β· 6,766,515 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8bc5fc1154c90f0e3b4893473e59df8871bc735f4558dc81ac34b3a13858209d
View on Chainz β†—

Height

#59,164

Difficulty

8.963611

Transactions

1

Size

199 B

Version

2

Bits

08f6af3b

Nonce

124

Timestamp

7/18/2013, 12:40:37 AM

Confirmations

6,766,515

Merkle Root

63f8c6123b1cd8189b22c9827bf2c2d7bcc1515b2843eb549578542f5664fa26
Transactions (1)
Coinbase63f8c6123b1cd8…78542f5664fa26
1 in β†’ 1 out12.4300 XPM109 B
ALrmUtTK…mrY2HuY9
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.

5.836 Γ— 10⁹⁴(95-digit number)
58362883141425833672…17585929971285588820
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
5.836 Γ— 10⁹⁴(95-digit number)
58362883141425833672…17585929971285588819
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.167 Γ— 10⁹⁡(96-digit number)
11672576628285166734…35171859942571177639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.334 Γ— 10⁹⁡(96-digit number)
23345153256570333468…70343719885142355279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.669 Γ— 10⁹⁡(96-digit number)
46690306513140666937…40687439770284710559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.338 Γ— 10⁹⁡(96-digit number)
93380613026281333875…81374879540569421119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.867 Γ— 10⁹⁢(97-digit number)
18676122605256266775…62749759081138842239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.735 Γ— 10⁹⁢(97-digit number)
37352245210512533550…25499518162277684479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.470 Γ— 10⁹⁢(97-digit number)
74704490421025067100…50999036324555368959
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 59164

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 8bc5fc1154c90f0e3b4893473e59df8871bc735f4558dc81ac34b3a13858209d

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 #59,164 on Chainz β†—
Circulating Supply:57,849,542 XPMΒ·at block #6,825,678 Β· updates every 60s
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