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Block #136,075

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/27/2013, 12:15:52 AM Β· Difficulty 9.8142 Β· 6,678,913 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6aa149c52b5631d1f3c8d5ce5cf258aeeba7d859a497da9435c913f54216b147
View on Chainz β†—

Height

#136,075

Difficulty

9.814182

Transactions

1

Size

197 B

Version

2

Bits

09d06e35

Nonce

255,896

Timestamp

8/27/2013, 12:15:52 AM

Confirmations

6,678,913

Merkle Root

fe659fb1c7ec2ece26a5c9d48f791d32a2dfdb7d9dafdde905c1dcfe48ab3d6f
Transactions (1)
Coinbasefe659fb1c7ec2e…c1dcfe48ab3d6f
1 in β†’ 1 out10.3700 XPM109 B
AQAhV6Gm…zPsSKfi5
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.

9.734 Γ— 10⁸⁹(90-digit number)
97343604856691202950…68635025618615903320
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
9.734 Γ— 10⁸⁹(90-digit number)
97343604856691202950…68635025618615903319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.946 Γ— 10⁹⁰(91-digit number)
19468720971338240590…37270051237231806639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.893 Γ— 10⁹⁰(91-digit number)
38937441942676481180…74540102474463613279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.787 Γ— 10⁹⁰(91-digit number)
77874883885352962360…49080204948927226559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.557 Γ— 10⁹¹(92-digit number)
15574976777070592472…98160409897854453119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.114 Γ— 10⁹¹(92-digit number)
31149953554141184944…96320819795708906239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.229 Γ— 10⁹¹(92-digit number)
62299907108282369888…92641639591417812479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.245 Γ— 10⁹²(93-digit number)
12459981421656473977…85283279182835624959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.491 Γ— 10⁹²(93-digit number)
24919962843312947955…70566558365671249919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.983 Γ— 10⁹²(93-digit number)
49839925686625895910…41133116731342499839
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 136075

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 6aa149c52b5631d1f3c8d5ce5cf258aeeba7d859a497da9435c913f54216b147

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 #136,075 on Chainz β†—
Circulating Supply:57,763,989 XPMΒ·at block #6,814,987 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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