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Block #148,475

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/3/2013, 6:43:39 PM Β· Difficulty 9.8544 Β· 6,666,625 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c810edd78b5cc785491158b29bfef63ff2ee051999f09938a7ffafbf51f40495
View on Chainz β†—

Height

#148,475

Difficulty

9.854352

Transactions

1

Size

200 B

Version

2

Bits

09dab6d4

Nonce

134,705

Timestamp

9/3/2013, 6:43:39 PM

Confirmations

6,666,625

Merkle Root

5a7b165a83b708b8b12f6ec2e2174a2e5ced1abdd9bd6d0bb43583ac1984e64d
Transactions (1)
Coinbase5a7b165a83b708…3583ac1984e64d
1 in β†’ 1 out10.2800 XPM109 B
ARdDiuG8…wggxf9Qh
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.

2.773 Γ— 10⁹⁢(97-digit number)
27730923600541916724…72074591518818035840
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
2.773 Γ— 10⁹⁢(97-digit number)
27730923600541916724…72074591518818035839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.546 Γ— 10⁹⁢(97-digit number)
55461847201083833448…44149183037636071679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.109 Γ— 10⁹⁷(98-digit number)
11092369440216766689…88298366075272143359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.218 Γ— 10⁹⁷(98-digit number)
22184738880433533379…76596732150544286719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.436 Γ— 10⁹⁷(98-digit number)
44369477760867066759…53193464301088573439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.873 Γ— 10⁹⁷(98-digit number)
88738955521734133518…06386928602177146879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.774 Γ— 10⁹⁸(99-digit number)
17747791104346826703…12773857204354293759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.549 Γ— 10⁹⁸(99-digit number)
35495582208693653407…25547714408708587519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.099 Γ— 10⁹⁸(99-digit number)
70991164417387306814…51095428817417175039
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 148475

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 c810edd78b5cc785491158b29bfef63ff2ee051999f09938a7ffafbf51f40495

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 #148,475 on Chainz β†—
Circulating Supply:57,764,889 XPMΒ·at block #6,815,099 Β· updates every 60s
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