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Block #140,679

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/29/2013, 7:45:45 PM Β· Difficulty 9.8337 Β· 6,654,040 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4e646f6f3262af4f0c0457955e084db03854927059e9eb392534ccc7c96bc28f
View on Chainz β†—

Height

#140,679

Difficulty

9.833693

Transactions

1

Size

198 B

Version

2

Bits

09d56ce4

Nonce

516,280

Timestamp

8/29/2013, 7:45:45 PM

Confirmations

6,654,040

Merkle Root

49d21a8b602fdfca27f3a4cb94de53ccbe19b4736fb181047a4bada3c54d01c4
Transactions (1)
Coinbase49d21a8b602fdf…4bada3c54d01c4
1 in β†’ 1 out10.3300 XPM109 B
AVB3GBxS…ux3ibfyg
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.

4.748 Γ— 10⁹²(93-digit number)
47486142901186301470…18980914017248450560
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
4.748 Γ— 10⁹²(93-digit number)
47486142901186301470…18980914017248450559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.497 Γ— 10⁹²(93-digit number)
94972285802372602940…37961828034496901119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.899 Γ— 10⁹³(94-digit number)
18994457160474520588…75923656068993802239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.798 Γ— 10⁹³(94-digit number)
37988914320949041176…51847312137987604479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.597 Γ— 10⁹³(94-digit number)
75977828641898082352…03694624275975208959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.519 Γ— 10⁹⁴(95-digit number)
15195565728379616470…07389248551950417919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.039 Γ— 10⁹⁴(95-digit number)
30391131456759232941…14778497103900835839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.078 Γ— 10⁹⁴(95-digit number)
60782262913518465882…29556994207801671679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.215 Γ— 10⁹⁡(96-digit number)
12156452582703693176…59113988415603343359
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 140679

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 4e646f6f3262af4f0c0457955e084db03854927059e9eb392534ccc7c96bc28f

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 #140,679 on Chainz β†—
Circulating Supply:57,601,801 XPMΒ·at block #6,794,718 Β· updates every 60s
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