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Block #73,732

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/21/2013, 7:31:17 AM Β· Difficulty 8.9950 Β· 6,722,552 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8b6015f90e852b5836370ff0f95bd7687300a8ebf1a89dc1400c10fcbcedff94
View on Chainz β†—

Height

#73,732

Difficulty

8.995026

Transactions

1

Size

197 B

Version

2

Bits

08feba09

Nonce

469

Timestamp

7/21/2013, 7:31:17 AM

Confirmations

6,722,552

Merkle Root

ecc767ffc0866301ceb701f670113e55867f4351e4ab8e2a1174b8f41293d3db
Transactions (1)
Coinbaseecc767ffc08663…74b8f41293d3db
1 in β†’ 1 out12.3400 XPM110 B
AJkJgvbD…5D37yqR6
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.

2.677 Γ— 10⁸⁷(88-digit number)
26771863799607506459…38868149084311948660
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
2.677 Γ— 10⁸⁷(88-digit number)
26771863799607506459…38868149084311948659
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.354 Γ— 10⁸⁷(88-digit number)
53543727599215012919…77736298168623897319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.070 Γ— 10⁸⁸(89-digit number)
10708745519843002583…55472596337247794639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.141 Γ— 10⁸⁸(89-digit number)
21417491039686005167…10945192674495589279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.283 Γ— 10⁸⁸(89-digit number)
42834982079372010335…21890385348991178559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.566 Γ— 10⁸⁸(89-digit number)
85669964158744020671…43780770697982357119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.713 Γ— 10⁸⁹(90-digit number)
17133992831748804134…87561541395964714239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.426 Γ— 10⁸⁹(90-digit number)
34267985663497608268…75123082791929428479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.853 Γ— 10⁸⁹(90-digit number)
68535971326995216537…50246165583858856959
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 73732

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 8b6015f90e852b5836370ff0f95bd7687300a8ebf1a89dc1400c10fcbcedff94

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 #73,732 on Chainz β†—
Circulating Supply:57,614,275 XPMΒ·at block #6,796,283 Β· updates every 60s
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