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Block #59,951

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/18/2013, 5:13:46 AM Β· Difficulty 8.9672 Β· 6,736,038 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
49f0d6f888f8b5a7a5e9cb93cc7e3698db003f8186bcd5f1e0ea34ed2029c968
View on Chainz β†—

Height

#59,951

Difficulty

8.967161

Transactions

1

Size

201 B

Version

2

Bits

08f797e5

Nonce

373

Timestamp

7/18/2013, 5:13:46 AM

Confirmations

6,736,038

Merkle Root

b08d865364a7f2b7d779aa2c5e105a9eea098954875e8787c1cc37273ecf23c1
Transactions (1)
Coinbaseb08d865364a7f2…cc37273ecf23c1
1 in β†’ 1 out12.4200 XPM110 B
AWq5ihMP…NAgyTJm5
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.

1.040 Γ— 10⁹⁸(99-digit number)
10403061907062672289…10102926681964754710
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.040 Γ— 10⁹⁸(99-digit number)
10403061907062672289…10102926681964754711
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.080 Γ— 10⁹⁸(99-digit number)
20806123814125344578…20205853363929509421
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.161 Γ— 10⁹⁸(99-digit number)
41612247628250689157…40411706727859018841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.322 Γ— 10⁹⁸(99-digit number)
83224495256501378315…80823413455718037681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.664 Γ— 10⁹⁹(100-digit number)
16644899051300275663…61646826911436075361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.328 Γ— 10⁹⁹(100-digit number)
33289798102600551326…23293653822872150721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.657 Γ— 10⁹⁹(100-digit number)
66579596205201102652…46587307645744301441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.331 Γ— 10¹⁰⁰(101-digit number)
13315919241040220530…93174615291488602881
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 59951

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 49f0d6f888f8b5a7a5e9cb93cc7e3698db003f8186bcd5f1e0ea34ed2029c968

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 #59,951 on Chainz β†—
Circulating Supply:57,612,007 XPMΒ·at block #6,795,988 Β· updates every 60s
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