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Block #155,236

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/8/2013, 4:54:47 AM Β· Difficulty 9.8655 Β· 6,671,795 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
639fb8ac81109d1275b3902c7ec63e7eee7d735c359d335b5d47cd27cb1741bd
View on Chainz β†—

Height

#155,236

Difficulty

9.865473

Transactions

1

Size

197 B

Version

2

Bits

09dd8f9f

Nonce

188,656

Timestamp

9/8/2013, 4:54:47 AM

Confirmations

6,671,795

Merkle Root

04540b411a9e5da000892009eb5c6436b051809b7240d6a553452e664e0d5da3
Transactions (1)
Coinbase04540b411a9e5d…452e664e0d5da3
1 in β†’ 1 out10.2600 XPM109 B
AGfxj4he…8ESKkS5f
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.

1.650 Γ— 10⁹⁰(91-digit number)
16503210419457607340…89130326770102724080
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
1.650 Γ— 10⁹⁰(91-digit number)
16503210419457607340…89130326770102724079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.300 Γ— 10⁹⁰(91-digit number)
33006420838915214680…78260653540205448159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.601 Γ— 10⁹⁰(91-digit number)
66012841677830429360…56521307080410896319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.320 Γ— 10⁹¹(92-digit number)
13202568335566085872…13042614160821792639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.640 Γ— 10⁹¹(92-digit number)
26405136671132171744…26085228321643585279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.281 Γ— 10⁹¹(92-digit number)
52810273342264343488…52170456643287170559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.056 Γ— 10⁹²(93-digit number)
10562054668452868697…04340913286574341119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.112 Γ— 10⁹²(93-digit number)
21124109336905737395…08681826573148682239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.224 Γ— 10⁹²(93-digit number)
42248218673811474790…17363653146297364479
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 155236

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 639fb8ac81109d1275b3902c7ec63e7eee7d735c359d335b5d47cd27cb1741bd

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 #155,236 on Chainz β†—
Circulating Supply:57,860,428 XPMΒ·at block #6,827,030 Β· updates every 60s
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