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Block #155,359

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/8/2013, 6:51:11 AM Β· Difficulty 9.8656 Β· 6,669,196 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7323785e73b2a94c8a18961d937d17a844be1d94e314f3e0b35e02d188e330e1
View on Chainz β†—

Height

#155,359

Difficulty

9.865633

Transactions

1

Size

197 B

Version

2

Bits

09dd9a27

Nonce

110,259

Timestamp

9/8/2013, 6:51:11 AM

Confirmations

6,669,196

Merkle Root

670b01f78cc43d69698724b183c2dd1782cd4378c3d14ed9ebb6cdfcbbd4c272
Transactions (1)
Coinbase670b01f78cc43d…b6cdfcbbd4c272
1 in β†’ 1 out10.2600 XPM109 B
ANGtmL1g…s5c9mevS
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.

8.163 Γ— 10⁹⁰(91-digit number)
81634598196497890005…10083969516131554800
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
8.163 Γ— 10⁹⁰(91-digit number)
81634598196497890005…10083969516131554799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.632 Γ— 10⁹¹(92-digit number)
16326919639299578001…20167939032263109599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.265 Γ— 10⁹¹(92-digit number)
32653839278599156002…40335878064526219199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.530 Γ— 10⁹¹(92-digit number)
65307678557198312004…80671756129052438399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.306 Γ— 10⁹²(93-digit number)
13061535711439662400…61343512258104876799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.612 Γ— 10⁹²(93-digit number)
26123071422879324801…22687024516209753599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.224 Γ— 10⁹²(93-digit number)
52246142845758649603…45374049032419507199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.044 Γ— 10⁹³(94-digit number)
10449228569151729920…90748098064839014399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.089 Γ— 10⁹³(94-digit number)
20898457138303459841…81496196129678028799
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 155359

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 7323785e73b2a94c8a18961d937d17a844be1d94e314f3e0b35e02d188e330e1

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 #155,359 on Chainz β†—
Circulating Supply:57,840,503 XPMΒ·at block #6,824,554 Β· updates every 60s
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