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Block #156,542

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/9/2013, 12:39:36 AM Β· Difficulty 9.8687 Β· 6,655,160 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
014efbd47d7a78aa2b62ba735cc7b238a84ed2088a30de07a18aece8c3f24a7c
View on Chainz β†—

Height

#156,542

Difficulty

9.868683

Transactions

1

Size

198 B

Version

2

Bits

09de620a

Nonce

98,012

Timestamp

9/9/2013, 12:39:36 AM

Confirmations

6,655,160

Merkle Root

06f35221d2d9c9edf34649d87abed3cebd08c77e32beee8f5761074fed14b916
Transactions (1)
Coinbase06f35221d2d9c9…61074fed14b916
1 in β†’ 1 out10.2500 XPM109 B
Aexc4U5C…VzkLuBQ9
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.

1.259 Γ— 10⁹²(93-digit number)
12590955420836592141…30558863486787788800
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
1.259 Γ— 10⁹²(93-digit number)
12590955420836592141…30558863486787788799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.518 Γ— 10⁹²(93-digit number)
25181910841673184283…61117726973575577599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.036 Γ— 10⁹²(93-digit number)
50363821683346368566…22235453947151155199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.007 Γ— 10⁹³(94-digit number)
10072764336669273713…44470907894302310399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.014 Γ— 10⁹³(94-digit number)
20145528673338547426…88941815788604620799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.029 Γ— 10⁹³(94-digit number)
40291057346677094853…77883631577209241599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.058 Γ— 10⁹³(94-digit number)
80582114693354189707…55767263154418483199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.611 Γ— 10⁹⁴(95-digit number)
16116422938670837941…11534526308836966399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.223 Γ— 10⁹⁴(95-digit number)
32232845877341675882…23069052617673932799
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 156542

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 014efbd47d7a78aa2b62ba735cc7b238a84ed2088a30de07a18aece8c3f24a7c

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 #156,542 on Chainz β†—
Circulating Supply:57,737,726 XPMΒ·at block #6,811,701 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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