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Block #78,332

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/22/2013, 7:04:16 PM Β· Difficulty 9.2292 Β· 6,717,376 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f516be480199cbbc0a225476f1a48c9e4644714429d9066ef0d0fe4f614d045b
View on Chainz β†—

Height

#78,332

Difficulty

9.229221

Transactions

2

Size

426 B

Version

2

Bits

093aae41

Nonce

34

Timestamp

7/22/2013, 7:04:16 PM

Confirmations

6,717,376

Merkle Root

3268fe8fb40aa6716f5012bd635882d3f829c6330c10cf271fc8a589bbd298c9
Transactions (2)
Coinbase7d92c608bdf172…d9f1cd6ed74bda
1 in β†’ 1 out11.7300 XPM110 B
AK1JUKWL…oPR4rN5o
f209872995f571…22358144da9963
1 in β†’ 2 out2.9267 XPM227 B
AXKq2kjv…6wC3gt4QAS1nhTbX…9RRfLTan
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.

1.906 Γ— 10⁹¹(92-digit number)
19067683856958942867…92956918677749965000
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
1.906 Γ— 10⁹¹(92-digit number)
19067683856958942867…92956918677749964999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.813 Γ— 10⁹¹(92-digit number)
38135367713917885735…85913837355499929999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.627 Γ— 10⁹¹(92-digit number)
76270735427835771470…71827674710999859999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.525 Γ— 10⁹²(93-digit number)
15254147085567154294…43655349421999719999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.050 Γ— 10⁹²(93-digit number)
30508294171134308588…87310698843999439999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.101 Γ— 10⁹²(93-digit number)
61016588342268617176…74621397687998879999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.220 Γ— 10⁹³(94-digit number)
12203317668453723435…49242795375997759999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.440 Γ— 10⁹³(94-digit number)
24406635336907446870…98485590751995519999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.881 Γ— 10⁹³(94-digit number)
48813270673814893741…96971181503991039999
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 78332

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 f516be480199cbbc0a225476f1a48c9e4644714429d9066ef0d0fe4f614d045b

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 #78,332 on Chainz β†—
Circulating Supply:57,609,737 XPMΒ·at block #6,795,707 Β· updates every 60s
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