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Block #72,471

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/21/2013, 12:23:35 AM Β· Difficulty 8.9941 Β· 6,733,154 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
355d6a9b5fb4eb2a41d954ec0d48baa9232130355cf5e4711c493c795c6817d9
View on Chainz β†—

Height

#72,471

Difficulty

8.994091

Transactions

1

Size

197 B

Version

2

Bits

08fe7cc7

Nonce

520

Timestamp

7/21/2013, 12:23:35 AM

Confirmations

6,733,154

Merkle Root

fb0164ff66f02f376539ddec4828699371e999ee6a19bd1155271308da9812c4
Transactions (1)
Coinbasefb0164ff66f02f…271308da9812c4
1 in β†’ 1 out12.3400 XPM110 B
APxUMipn…2zpbPwcA
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.

2.085 Γ— 10⁸⁷(88-digit number)
20851449932699645220…66861393869337992960
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
2.085 Γ— 10⁸⁷(88-digit number)
20851449932699645220…66861393869337992959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.170 Γ— 10⁸⁷(88-digit number)
41702899865399290441…33722787738675985919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.340 Γ— 10⁸⁷(88-digit number)
83405799730798580883…67445575477351971839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.668 Γ— 10⁸⁸(89-digit number)
16681159946159716176…34891150954703943679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.336 Γ— 10⁸⁸(89-digit number)
33362319892319432353…69782301909407887359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.672 Γ— 10⁸⁸(89-digit number)
66724639784638864706…39564603818815774719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.334 Γ— 10⁸⁹(90-digit number)
13344927956927772941…79129207637631549439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.668 Γ— 10⁸⁹(90-digit number)
26689855913855545882…58258415275263098879
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8
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 72471

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 355d6a9b5fb4eb2a41d954ec0d48baa9232130355cf5e4711c493c795c6817d9

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 #72,471 on Chainz β†—
Circulating Supply:57,689,074 XPMΒ·at block #6,805,624 Β· updates every 60s
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