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Block #104,818

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/8/2013, 5:44:21 AM Β· Difficulty 9.5675 Β· 6,712,393 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0d739700dcfaf68c25ef3f601ff1c28217a693fce83272fa4557c51c5fce0f71
View on Chainz β†—

Height

#104,818

Difficulty

9.567455

Transactions

1

Size

200 B

Version

2

Bits

099144c3

Nonce

46,143

Timestamp

8/8/2013, 5:44:21 AM

Confirmations

6,712,393

Merkle Root

1f22f8001e84418d3dcd06e75f91d8ec1bfaf07c49895857c9e91255185241ad
Transactions (1)
Coinbase1f22f8001e8441…e91255185241ad
1 in β†’ 1 out10.9100 XPM109 B
AXvMMum1…y1ajpFRb
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.

1.151 Γ— 10⁹⁷(98-digit number)
11510214292591763564…50097756762252033840
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
1.151 Γ— 10⁹⁷(98-digit number)
11510214292591763564…50097756762252033841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.302 Γ— 10⁹⁷(98-digit number)
23020428585183527129…00195513524504067681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.604 Γ— 10⁹⁷(98-digit number)
46040857170367054259…00391027049008135361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.208 Γ— 10⁹⁷(98-digit number)
92081714340734108519…00782054098016270721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.841 Γ— 10⁹⁸(99-digit number)
18416342868146821703…01564108196032541441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.683 Γ— 10⁹⁸(99-digit number)
36832685736293643407…03128216392065082881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.366 Γ— 10⁹⁸(99-digit number)
73665371472587286815…06256432784130165761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.473 Γ— 10⁹⁹(100-digit number)
14733074294517457363…12512865568260331521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.946 Γ— 10⁹⁹(100-digit number)
29466148589034914726…25025731136520663041
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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 9
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 104818

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 0d739700dcfaf68c25ef3f601ff1c28217a693fce83272fa4557c51c5fce0f71

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 #104,818 on Chainz β†—
Circulating Supply:57,781,727 XPMΒ·at block #6,817,210 Β· updates every 60s
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