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Block #58,779

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/17/2013, 10:35:55 PM Β· Difficulty 8.9617 Β· 6,768,120 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7508ceecaaf7e8169af4032367811595dc8eface68cd42bd7d611b18c6672f20
View on Chainz β†—

Height

#58,779

Difficulty

8.961673

Transactions

2

Size

359 B

Version

2

Bits

08f63036

Nonce

78

Timestamp

7/17/2013, 10:35:55 PM

Confirmations

6,768,120

Merkle Root

21a090da7afb6eec0cd82d8cb85df78f49814c36c2df37103d726ca5ea5d202c
Transactions (2)
Coinbase5655d43500f617…4e04df0c0b2d1f
1 in β†’ 1 out12.4400 XPM110 B
AVK8gCEy…o9Ce5V89
74db3df001a688…f8597ac7b09183
1 in β†’ 1 out13.5200 XPM158 B
AR69AesG…rB4CzTXs
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.

5.015 Γ— 10⁹⁢(97-digit number)
50158145610927571517…01903894362901601520
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
5.015 Γ— 10⁹⁢(97-digit number)
50158145610927571517…01903894362901601519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.003 Γ— 10⁹⁷(98-digit number)
10031629122185514303…03807788725803203039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.006 Γ— 10⁹⁷(98-digit number)
20063258244371028607…07615577451606406079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.012 Γ— 10⁹⁷(98-digit number)
40126516488742057214…15231154903212812159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.025 Γ— 10⁹⁷(98-digit number)
80253032977484114428…30462309806425624319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.605 Γ— 10⁹⁸(99-digit number)
16050606595496822885…60924619612851248639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.210 Γ— 10⁹⁸(99-digit number)
32101213190993645771…21849239225702497279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.420 Γ— 10⁹⁸(99-digit number)
64202426381987291542…43698478451404994559
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 58779

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 7508ceecaaf7e8169af4032367811595dc8eface68cd42bd7d611b18c6672f20

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 #58,779 on Chainz β†—
Circulating Supply:57,859,358 XPMΒ·at block #6,826,898 Β· updates every 60s
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