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Block #149,014

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/4/2013, 2:21:22 AM Β· Difficulty 9.8567 Β· 6,666,982 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
55cd753582ed97576ea300d643a36b2afa458bbbc7e202e4a7f8b80a97e5c53e
View on Chainz β†—

Height

#149,014

Difficulty

9.856694

Transactions

1

Size

202 B

Version

2

Bits

09db504c

Nonce

526,966

Timestamp

9/4/2013, 2:21:22 AM

Confirmations

6,666,982

Merkle Root

233981b2b30ce3c803c051c5caf2f5e15b31befbb383df6e28a72a2bfcd9890b
Transactions (1)
Coinbase233981b2b30ce3…a72a2bfcd9890b
1 in β†’ 1 out10.2800 XPM112 B
AT5A2KL6…CT16n6i2
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.

1.054 Γ— 10⁹⁡(96-digit number)
10544507018400372312…62238414208924856360
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
1.054 Γ— 10⁹⁡(96-digit number)
10544507018400372312…62238414208924856361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.108 Γ— 10⁹⁡(96-digit number)
21089014036800744625…24476828417849712721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.217 Γ— 10⁹⁡(96-digit number)
42178028073601489251…48953656835699425441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.435 Γ— 10⁹⁡(96-digit number)
84356056147202978502…97907313671398850881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.687 Γ— 10⁹⁢(97-digit number)
16871211229440595700…95814627342797701761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.374 Γ— 10⁹⁢(97-digit number)
33742422458881191401…91629254685595403521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.748 Γ— 10⁹⁢(97-digit number)
67484844917762382802…83258509371190807041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.349 Γ— 10⁹⁷(98-digit number)
13496968983552476560…66517018742381614081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.699 Γ— 10⁹⁷(98-digit number)
26993937967104953120…33034037484763228161
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 149014

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 55cd753582ed97576ea300d643a36b2afa458bbbc7e202e4a7f8b80a97e5c53e

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 #149,014 on Chainz β†—
Circulating Supply:57,772,083 XPMΒ·at block #6,815,995 Β· updates every 60s
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