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Block #69,706

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/20/2013, 10:04:40 AM Β· Difficulty 8.9913 Β· 6,725,898 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d954611527d2f733612e2f5ce87a251ba71df0c94e7fa9981af03e71807faecc
View on Chainz β†—

Height

#69,706

Difficulty

8.991274

Transactions

1

Size

198 B

Version

2

Bits

08fdc424

Nonce

1,165

Timestamp

7/20/2013, 10:04:40 AM

Confirmations

6,725,898

Merkle Root

fa040de75f58d5c4d014ceedb93af87ece2a6db62c8a802df4553f30eb206fe0
Transactions (1)
Coinbasefa040de75f58d5…553f30eb206fe0
1 in β†’ 1 out12.3500 XPM110 B
AapcK8f4…JjJZmYcx
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.

2.391 Γ— 10⁹⁰(91-digit number)
23914117739369979203…78281998707058361400
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
2.391 Γ— 10⁹⁰(91-digit number)
23914117739369979203…78281998707058361399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.782 Γ— 10⁹⁰(91-digit number)
47828235478739958406…56563997414116722799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.565 Γ— 10⁹⁰(91-digit number)
95656470957479916813…13127994828233445599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.913 Γ— 10⁹¹(92-digit number)
19131294191495983362…26255989656466891199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.826 Γ— 10⁹¹(92-digit number)
38262588382991966725…52511979312933782399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.652 Γ— 10⁹¹(92-digit number)
76525176765983933451…05023958625867564799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.530 Γ— 10⁹²(93-digit number)
15305035353196786690…10047917251735129599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.061 Γ— 10⁹²(93-digit number)
30610070706393573380…20095834503470259199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.122 Γ— 10⁹²(93-digit number)
61220141412787146760…40191669006940518399
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 69706

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 d954611527d2f733612e2f5ce87a251ba71df0c94e7fa9981af03e71807faecc

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 #69,706 on Chainz β†—
Circulating Supply:57,608,895 XPMΒ·at block #6,795,603 Β· updates every 60s
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