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Block #144,107

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/1/2013, 2:47:49 AM Β· Difficulty 9.8379 Β· 6,672,052 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
516345393dd514a4bc02bc7ffe13278ec2ec571108face046f4b82fb70adeca5
View on Chainz β†—

Height

#144,107

Difficulty

9.837888

Transactions

1

Size

198 B

Version

2

Bits

09d67fcf

Nonce

185,260

Timestamp

9/1/2013, 2:47:49 AM

Confirmations

6,672,052

Merkle Root

9dc78f1db4d619fefa3894de0cf5392e6fa1ada4ff9aa36d8e4531b37963b55d
Transactions (1)
Coinbase9dc78f1db4d619…4531b37963b55d
1 in β†’ 1 out10.3200 XPM109 B
AZEUcnJn…WVjTRd4v
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.

1.931 Γ— 10⁹²(93-digit number)
19315838520834534319…01698631544035577120
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
1.931 Γ— 10⁹²(93-digit number)
19315838520834534319…01698631544035577119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.863 Γ— 10⁹²(93-digit number)
38631677041669068638…03397263088071154239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.726 Γ— 10⁹²(93-digit number)
77263354083338137276…06794526176142308479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.545 Γ— 10⁹³(94-digit number)
15452670816667627455…13589052352284616959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.090 Γ— 10⁹³(94-digit number)
30905341633335254910…27178104704569233919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.181 Γ— 10⁹³(94-digit number)
61810683266670509821…54356209409138467839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.236 Γ— 10⁹⁴(95-digit number)
12362136653334101964…08712418818276935679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.472 Γ— 10⁹⁴(95-digit number)
24724273306668203928…17424837636553871359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.944 Γ— 10⁹⁴(95-digit number)
49448546613336407856…34849675273107742719
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 144107

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 516345393dd514a4bc02bc7ffe13278ec2ec571108face046f4b82fb70adeca5

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 #144,107 on Chainz β†—
Circulating Supply:57,773,395 XPMΒ·at block #6,816,158 Β· updates every 60s
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