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Block #129,460

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/22/2013, 10:44:11 PM Β· Difficulty 9.7835 Β· 6,696,232 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
133b852d9484bae2051629a86dab08fa0141f79d9aeaff7c2a6801e2f6fefc09
View on Chainz β†—

Height

#129,460

Difficulty

9.783548

Transactions

1

Size

200 B

Version

2

Bits

09c896a2

Nonce

242,642

Timestamp

8/22/2013, 10:44:11 PM

Confirmations

6,696,232

Merkle Root

402c2369c0b4ac7cc490aecf879a9f6d422a600f2873582d0f0b1e342bee9919
Transactions (1)
Coinbase402c2369c0b4ac…0b1e342bee9919
1 in β†’ 1 out10.4300 XPM109 B
AXJUTcXK…VsMN2v9N
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.

5.966 Γ— 10⁹⁷(98-digit number)
59664491734762986927…80850158266102391640
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
5.966 Γ— 10⁹⁷(98-digit number)
59664491734762986927…80850158266102391641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.193 Γ— 10⁹⁸(99-digit number)
11932898346952597385…61700316532204783281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.386 Γ— 10⁹⁸(99-digit number)
23865796693905194770…23400633064409566561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.773 Γ— 10⁹⁸(99-digit number)
47731593387810389541…46801266128819133121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.546 Γ— 10⁹⁸(99-digit number)
95463186775620779083…93602532257638266241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.909 Γ— 10⁹⁹(100-digit number)
19092637355124155816…87205064515276532481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.818 Γ— 10⁹⁹(100-digit number)
38185274710248311633…74410129030553064961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.637 Γ— 10⁹⁹(100-digit number)
76370549420496623266…48820258061106129921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.527 Γ— 10¹⁰⁰(101-digit number)
15274109884099324653…97640516122212259841
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 129460

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 133b852d9484bae2051629a86dab08fa0141f79d9aeaff7c2a6801e2f6fefc09

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 #129,460 on Chainz β†—
Circulating Supply:57,849,647 XPMΒ·at block #6,825,691 Β· updates every 60s
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