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Block #154,556

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/7/2013, 6:06:17 PM Β· Difficulty 9.8646 Β· 6,641,028 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
662e488b35ff30f7935ce78c78a43fc936c6cc7773cf6ce599ecc064c13abe9d
View on Chainz β†—

Height

#154,556

Difficulty

9.864596

Transactions

2

Size

1.14 KB

Version

2

Bits

09dd5628

Nonce

95,532

Timestamp

9/7/2013, 6:06:17 PM

Confirmations

6,641,028

Merkle Root

3391299655cb0a4593495e5aeb644cff4959f8b978d8e7dde2afd93624ba94ea
Transactions (2)
Coinbase7fa352cb154274…820cfe8022c1ec
1 in β†’ 1 out10.2700 XPM109 B
AULL9B6R…thBLx9Hq
5e6c32a68e30cc…a5b30a16054260
6 in β†’ 2 out12.0780 XPM968 B
AWtMQ9ge…ouJcPoiFAGBaq3YB…99rcvMMP
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.

1.391 Γ— 10⁹³(94-digit number)
13916141372661138946…96791575865700770560
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
1.391 Γ— 10⁹³(94-digit number)
13916141372661138946…96791575865700770561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.783 Γ— 10⁹³(94-digit number)
27832282745322277892…93583151731401541121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.566 Γ— 10⁹³(94-digit number)
55664565490644555784…87166303462803082241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.113 Γ— 10⁹⁴(95-digit number)
11132913098128911156…74332606925606164481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.226 Γ— 10⁹⁴(95-digit number)
22265826196257822313…48665213851212328961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.453 Γ— 10⁹⁴(95-digit number)
44531652392515644627…97330427702424657921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.906 Γ— 10⁹⁴(95-digit number)
89063304785031289255…94660855404849315841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.781 Γ— 10⁹⁡(96-digit number)
17812660957006257851…89321710809698631681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.562 Γ— 10⁹⁡(96-digit number)
35625321914012515702…78643421619397263361
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 154556

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 662e488b35ff30f7935ce78c78a43fc936c6cc7773cf6ce599ecc064c13abe9d

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 #154,556 on Chainz β†—
Circulating Supply:57,608,734 XPMΒ·at block #6,795,583 Β· updates every 60s
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