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Block #138,313

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/28/2013, 8:24:25 AM Β· Difficulty 9.8253 Β· 6,678,771 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6ce0897b5e4a8b56759b0692b166b5660747fd97a96fbeefb3eb6e3408367734
View on Chainz β†—

Height

#138,313

Difficulty

9.825322

Transactions

2

Size

358 B

Version

2

Bits

09d3484b

Nonce

12,478

Timestamp

8/28/2013, 8:24:25 AM

Confirmations

6,678,771

Merkle Root

ba969ea99d8965d84e114ad371c10456dec556cc25c8fe922906d9817f16a098
Transactions (2)
Coinbasef979ee4d5c8bd8…0f94f228797976
1 in β†’ 1 out10.3500 XPM109 B
ALJ24E54…CM192Nmg
f9b694e0aabeab…1e8e3b43cb36cc
1 in β†’ 1 out10.3700 XPM159 B
AQj5CF31…Sfv2KzXY
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.

1.700 Γ— 10⁹⁡(96-digit number)
17004489726917263175…38218221823998123520
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
1.700 Γ— 10⁹⁡(96-digit number)
17004489726917263175…38218221823998123521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.400 Γ— 10⁹⁡(96-digit number)
34008979453834526351…76436443647996247041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.801 Γ— 10⁹⁡(96-digit number)
68017958907669052703…52872887295992494081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.360 Γ— 10⁹⁢(97-digit number)
13603591781533810540…05745774591984988161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.720 Γ— 10⁹⁢(97-digit number)
27207183563067621081…11491549183969976321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.441 Γ— 10⁹⁢(97-digit number)
54414367126135242162…22983098367939952641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.088 Γ— 10⁹⁷(98-digit number)
10882873425227048432…45966196735879905281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.176 Γ— 10⁹⁷(98-digit number)
21765746850454096864…91932393471759810561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.353 Γ— 10⁹⁷(98-digit number)
43531493700908193729…83864786943519621121
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 138313

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 6ce0897b5e4a8b56759b0692b166b5660747fd97a96fbeefb3eb6e3408367734

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 #138,313 on Chainz β†—
Circulating Supply:57,780,710 XPMΒ·at block #6,817,083 Β· updates every 60s
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