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Block #152,869

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/6/2013, 2:57:11 PM Β· Difficulty 9.8630 Β· 6,647,673 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a8797ba3d70f0c529ca020bce9c6dd0ae90ff463a4311ea63aba4d2e9a827420
View on Chainz β†—

Height

#152,869

Difficulty

9.862977

Transactions

1

Size

203 B

Version

2

Bits

09dcec13

Nonce

33,556,803

Timestamp

9/6/2013, 2:57:11 PM

Confirmations

6,647,673

Merkle Root

3710982102f25ed9dba493238e9ffc0d8c81e3ac6c1b6e169dfc1ddfff576375
Transactions (1)
Coinbase3710982102f25e…fc1ddfff576375
1 in β†’ 1 out10.2600 XPM112 B
AT5A2KL6…CT16n6i2
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.

3.946 Γ— 10⁹⁢(97-digit number)
39468314874944589521…04046529839202513920
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
3.946 Γ— 10⁹⁢(97-digit number)
39468314874944589521…04046529839202513921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.893 Γ— 10⁹⁢(97-digit number)
78936629749889179043…08093059678405027841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.578 Γ— 10⁹⁷(98-digit number)
15787325949977835808…16186119356810055681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.157 Γ— 10⁹⁷(98-digit number)
31574651899955671617…32372238713620111361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.314 Γ— 10⁹⁷(98-digit number)
63149303799911343234…64744477427240222721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.262 Γ— 10⁹⁸(99-digit number)
12629860759982268646…29488954854480445441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.525 Γ— 10⁹⁸(99-digit number)
25259721519964537293…58977909708960890881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.051 Γ— 10⁹⁸(99-digit number)
50519443039929074587…17955819417921781761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.010 Γ— 10⁹⁹(100-digit number)
10103888607985814917…35911638835843563521
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 152869

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 a8797ba3d70f0c529ca020bce9c6dd0ae90ff463a4311ea63aba4d2e9a827420

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 #152,869 on Chainz β†—
Circulating Supply:57,648,399 XPMΒ·at block #6,800,541 Β· updates every 60s
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