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Block #76,744

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/22/2013, 3:38:08 AM Β· Difficulty 9.1209 Β· 6,725,728 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a5417a112fd2b5e76470ae3f992dd16d5c2242dabba75b4f898c0eb51d778e9b
View on Chainz β†—

Height

#76,744

Difficulty

9.120900

Transactions

1

Size

203 B

Version

2

Bits

091ef348

Nonce

259

Timestamp

7/22/2013, 3:38:08 AM

Confirmations

6,725,728

Merkle Root

de2f315f59606da9856c38adc72af9d2053a17fa6111a5ccbb93d531e4e01eaa
Transactions (1)
Coinbasede2f315f59606d…93d531e4e01eaa
1 in β†’ 1 out12.0000 XPM109 B
AVtfr3G7…MXEF7aJ9
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.

6.644 Γ— 10¹⁰³(104-digit number)
66446160907670167921…87947138870574416540
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
6.644 Γ— 10¹⁰³(104-digit number)
66446160907670167921…87947138870574416539
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.328 Γ— 10¹⁰⁴(105-digit number)
13289232181534033584…75894277741148833079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.657 Γ— 10¹⁰⁴(105-digit number)
26578464363068067168…51788555482297666159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.315 Γ— 10¹⁰⁴(105-digit number)
53156928726136134337…03577110964595332319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.063 Γ— 10¹⁰⁡(106-digit number)
10631385745227226867…07154221929190664639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.126 Γ— 10¹⁰⁡(106-digit number)
21262771490454453734…14308443858381329279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.252 Γ— 10¹⁰⁡(106-digit number)
42525542980908907469…28616887716762658559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.505 Γ— 10¹⁰⁡(106-digit number)
85051085961817814939…57233775433525317119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.701 Γ— 10¹⁰⁢(107-digit number)
17010217192363562987…14467550867050634239
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 76744

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 a5417a112fd2b5e76470ae3f992dd16d5c2242dabba75b4f898c0eb51d778e9b

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 #76,744 on Chainz β†—
Circulating Supply:57,663,787 XPMΒ·at block #6,802,471 Β· updates every 60s
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