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Block #135,117

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/26/2013, 10:46:38 AM Β· Difficulty 9.8085 Β· 6,690,013 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6d59ee35383aac044b315577ca0162e586a98fea5f6d7d95debaeffa29b091e3
View on Chainz β†—

Height

#135,117

Difficulty

9.808529

Transactions

1

Size

204 B

Version

2

Bits

09cefbca

Nonce

94,557

Timestamp

8/26/2013, 10:46:38 AM

Confirmations

6,690,013

Merkle Root

05103729c089fd018e16048c51086305e13da8114b16a124ae153c23b12907e6
Transactions (1)
Coinbase05103729c089fd…153c23b12907e6
1 in β†’ 1 out10.3800 XPM112 B
AT5A2KL6…CT16n6i2
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.

2.448 Γ— 10⁹⁸(99-digit number)
24482696654999356083…87764776843913189320
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
2.448 Γ— 10⁹⁸(99-digit number)
24482696654999356083…87764776843913189319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.896 Γ— 10⁹⁸(99-digit number)
48965393309998712167…75529553687826378639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.793 Γ— 10⁹⁸(99-digit number)
97930786619997424335…51059107375652757279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.958 Γ— 10⁹⁹(100-digit number)
19586157323999484867…02118214751305514559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.917 Γ— 10⁹⁹(100-digit number)
39172314647998969734…04236429502611029119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.834 Γ— 10⁹⁹(100-digit number)
78344629295997939468…08472859005222058239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.566 Γ— 10¹⁰⁰(101-digit number)
15668925859199587893…16945718010444116479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.133 Γ— 10¹⁰⁰(101-digit number)
31337851718399175787…33891436020888232959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.267 Γ— 10¹⁰⁰(101-digit number)
62675703436798351574…67782872041776465919
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 135117

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 6d59ee35383aac044b315577ca0162e586a98fea5f6d7d95debaeffa29b091e3

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 #135,117 on Chainz β†—
Circulating Supply:57,845,124 XPMΒ·at block #6,825,129 Β· updates every 60s
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