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Block #75,503

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/21/2013, 4:51:50 PM Β· Difficulty 9.0102 Β· 6,724,653 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d35c9949bfad8cdc711e804d09abae0d6cd6a2ae2f3389d4bc9ebfa0eae02150
View on Chainz β†—

Height

#75,503

Difficulty

9.010226

Transactions

2

Size

363 B

Version

2

Bits

09029e2e

Nonce

599

Timestamp

7/21/2013, 4:51:50 PM

Confirmations

6,724,653

Merkle Root

996311ca188856906b57f91154322070ba5e3fe08b1f532de8ab4cae89ce916a
Transactions (2)
Coinbasebf4ae513cee3d4…07bf439ab0e940
1 in β†’ 1 out12.3100 XPM110 B
ASC1oTrB…xK29H933
da372cad4aa717…4a1710fe25d522
1 in β†’ 1 out12.3400 XPM159 B
AHhBD3ym…9JwgAcof
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.

1.662 Γ— 10¹⁰⁡(106-digit number)
16625260271173976882…25732096427270783320
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
1.662 Γ— 10¹⁰⁡(106-digit number)
16625260271173976882…25732096427270783319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.325 Γ— 10¹⁰⁡(106-digit number)
33250520542347953765…51464192854541566639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.650 Γ— 10¹⁰⁡(106-digit number)
66501041084695907530…02928385709083133279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.330 Γ— 10¹⁰⁢(107-digit number)
13300208216939181506…05856771418166266559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.660 Γ— 10¹⁰⁢(107-digit number)
26600416433878363012…11713542836332533119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.320 Γ— 10¹⁰⁢(107-digit number)
53200832867756726024…23427085672665066239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.064 Γ— 10¹⁰⁷(108-digit number)
10640166573551345204…46854171345330132479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.128 Γ— 10¹⁰⁷(108-digit number)
21280333147102690409…93708342690660264959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.256 Γ— 10¹⁰⁷(108-digit number)
42560666294205380819…87416685381320529919
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 75503

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 d35c9949bfad8cdc711e804d09abae0d6cd6a2ae2f3389d4bc9ebfa0eae02150

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 #75,503 on Chainz β†—
Circulating Supply:57,645,313 XPMΒ·at block #6,800,155 Β· updates every 60s
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