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Block #155,182

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/8/2013, 4:01:59 AM Β· Difficulty 9.8654 Β· 6,645,355 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5e268cbea781e3c1b815b8209e82cd24be71553bbca22e435ef49cb212d27dde
View on Chainz β†—

Height

#155,182

Difficulty

9.865415

Transactions

1

Size

198 B

Version

2

Bits

09dd8bd2

Nonce

73,086

Timestamp

9/8/2013, 4:01:59 AM

Confirmations

6,645,355

Merkle Root

d087ebc445ca8514d61d1c753bdc89ec82cd9663786b86cab5d909ef4fab2b31
Transactions (1)
Coinbased087ebc445ca85…d909ef4fab2b31
1 in β†’ 1 out10.2600 XPM109 B
AP91QEDQ…W6JZAB9n
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.

2.596 Γ— 10⁹²(93-digit number)
25960741895787294183…48961174423596584640
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
2.596 Γ— 10⁹²(93-digit number)
25960741895787294183…48961174423596584639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.192 Γ— 10⁹²(93-digit number)
51921483791574588366…97922348847193169279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.038 Γ— 10⁹³(94-digit number)
10384296758314917673…95844697694386338559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.076 Γ— 10⁹³(94-digit number)
20768593516629835346…91689395388772677119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.153 Γ— 10⁹³(94-digit number)
41537187033259670693…83378790777545354239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.307 Γ— 10⁹³(94-digit number)
83074374066519341386…66757581555090708479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.661 Γ— 10⁹⁴(95-digit number)
16614874813303868277…33515163110181416959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.322 Γ— 10⁹⁴(95-digit number)
33229749626607736554…67030326220362833919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.645 Γ— 10⁹⁴(95-digit number)
66459499253215473108…34060652440725667839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.329 Γ— 10⁹⁡(96-digit number)
13291899850643094621…68121304881451335679
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 155182

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 5e268cbea781e3c1b815b8209e82cd24be71553bbca22e435ef49cb212d27dde

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 #155,182 on Chainz β†—
Circulating Supply:57,648,358 XPMΒ·at block #6,800,536 Β· updates every 60s
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