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Block #141,704

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/30/2013, 12:00:49 PM Β· Difficulty 9.8353 Β· 6,683,086 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c7dbba28cb8543c6dce0f8236eca28ea302fc6db888508340a79de9370d7d4b9
View on Chainz β†—

Height

#141,704

Difficulty

9.835310

Transactions

1

Size

201 B

Version

2

Bits

09d5d6e6

Nonce

54,174

Timestamp

8/30/2013, 12:00:49 PM

Confirmations

6,683,086

Merkle Root

6cd648db2a3e5cef7247532200dbd902d65aae23e41b67e1b650343092eb2d2a
Transactions (1)
Coinbase6cd648db2a3e5c…50343092eb2d2a
1 in β†’ 1 out10.3200 XPM109 B
Abggtsno…ktHCYqnX
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.

2.473 Γ— 10⁹⁸(99-digit number)
24732848370197964684…48034819138585687500
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
2.473 Γ— 10⁹⁸(99-digit number)
24732848370197964684…48034819138585687499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.946 Γ— 10⁹⁸(99-digit number)
49465696740395929369…96069638277171374999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.893 Γ— 10⁹⁸(99-digit number)
98931393480791858739…92139276554342749999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.978 Γ— 10⁹⁹(100-digit number)
19786278696158371747…84278553108685499999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.957 Γ— 10⁹⁹(100-digit number)
39572557392316743495…68557106217370999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.914 Γ— 10⁹⁹(100-digit number)
79145114784633486991…37114212434741999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.582 Γ— 10¹⁰⁰(101-digit number)
15829022956926697398…74228424869483999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.165 Γ— 10¹⁰⁰(101-digit number)
31658045913853394796…48456849738967999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.331 Γ— 10¹⁰⁰(101-digit number)
63316091827706789592…96913699477935999999
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 141704

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 c7dbba28cb8543c6dce0f8236eca28ea302fc6db888508340a79de9370d7d4b9

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 #141,704 on Chainz β†—
Circulating Supply:57,842,395 XPMΒ·at block #6,824,789 Β· updates every 60s
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