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Block #73,153

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/21/2013, 4:15:31 AM Β· Difficulty 8.9946 Β· 6,738,457 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9d8b77e6379df25b5ce410b6e973bdb2f7e034bad5d86a940e4e40fc1e08d832
View on Chainz β†—

Height

#73,153

Difficulty

8.994616

Transactions

1

Size

201 B

Version

2

Bits

08fe9f24

Nonce

36

Timestamp

7/21/2013, 4:15:31 AM

Confirmations

6,738,457

Merkle Root

c90d672c6374b119fc39f4787625d5790040b57856856c77af3e0431b6984b2c
Transactions (1)
Coinbasec90d672c6374b1…3e0431b6984b2c
1 in β†’ 1 out12.3400 XPM110 B
AYFKLaF4…VzJhmYvm
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.

3.418 Γ— 10⁹⁢(97-digit number)
34186905130114099599…64350091766411802060
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
3.418 Γ— 10⁹⁢(97-digit number)
34186905130114099599…64350091766411802059
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.837 Γ— 10⁹⁢(97-digit number)
68373810260228199198…28700183532823604119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.367 Γ— 10⁹⁷(98-digit number)
13674762052045639839…57400367065647208239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.734 Γ— 10⁹⁷(98-digit number)
27349524104091279679…14800734131294416479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.469 Γ— 10⁹⁷(98-digit number)
54699048208182559358…29601468262588832959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.093 Γ— 10⁹⁸(99-digit number)
10939809641636511871…59202936525177665919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.187 Γ— 10⁹⁸(99-digit number)
21879619283273023743…18405873050355331839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.375 Γ— 10⁹⁸(99-digit number)
43759238566546047486…36811746100710663679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.751 Γ— 10⁹⁸(99-digit number)
87518477133092094973…73623492201421327359
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 73153

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 9d8b77e6379df25b5ce410b6e973bdb2f7e034bad5d86a940e4e40fc1e08d832

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 #73,153 on Chainz β†—
Circulating Supply:57,736,993 XPMΒ·at block #6,811,609 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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