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Block #122,636

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/18/2013, 2:47:19 PM Β· Difficulty 9.7564 Β· 6,678,273 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
14d19bca103f54ec8d0f7f3efe718f02a00ef0b7be2f542a7b3dc6d38caba08e
View on Chainz β†—

Height

#122,636

Difficulty

9.756419

Transactions

1

Size

200 B

Version

2

Bits

09c1a4ae

Nonce

164,318

Timestamp

8/18/2013, 2:47:19 PM

Confirmations

6,678,273

Merkle Root

7ef78eedb9167669d072a1ed92cf66a512621217b1f12c8da1e00bce6109808d
Transactions (1)
Coinbase7ef78eedb91676…e00bce6109808d
1 in β†’ 1 out10.4900 XPM109 B
AeL3h4ur…n29hApqS
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.

1.034 Γ— 10⁹⁸(99-digit number)
10349401654659386770…65307569767142213020
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
1.034 Γ— 10⁹⁸(99-digit number)
10349401654659386770…65307569767142213021
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.069 Γ— 10⁹⁸(99-digit number)
20698803309318773541…30615139534284426041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.139 Γ— 10⁹⁸(99-digit number)
41397606618637547082…61230279068568852081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.279 Γ— 10⁹⁸(99-digit number)
82795213237275094164…22460558137137704161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.655 Γ— 10⁹⁹(100-digit number)
16559042647455018832…44921116274275408321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.311 Γ— 10⁹⁹(100-digit number)
33118085294910037665…89842232548550816641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.623 Γ— 10⁹⁹(100-digit number)
66236170589820075331…79684465097101633281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.324 Γ— 10¹⁰⁰(101-digit number)
13247234117964015066…59368930194203266561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.649 Γ— 10¹⁰⁰(101-digit number)
26494468235928030132…18737860388406533121
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 122636

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 14d19bca103f54ec8d0f7f3efe718f02a00ef0b7be2f542a7b3dc6d38caba08e

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 #122,636 on Chainz β†—
Circulating Supply:57,651,333 XPMΒ·at block #6,800,908 Β· updates every 60s
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