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Block #663,042

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/5/2014, 1:36:35 AM Β· Difficulty 10.9571 Β· 6,133,295 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
41f78d83449d78c9139a2aae72f9c8259e3662a0f9a354797dfa8d3c0d00c4ba
View on Chainz β†—

Height

#663,042

Difficulty

10.957102

Transactions

1

Size

207 B

Version

2

Bits

0af504ab

Nonce

127,110,393

Timestamp

8/5/2014, 1:36:35 AM

Confirmations

6,133,295

Merkle Root

b23b8f5d9c34d5efaaef9e4c5e2287c38eb5f16bb6b61c732cfe7390ca23c946
Transactions (1)
Coinbaseb23b8f5d9c34d5…fe7390ca23c946
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
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.

1.965 Γ— 10⁹⁷(98-digit number)
19650855617425721106…97854234057323939840
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
1.965 Γ— 10⁹⁷(98-digit number)
19650855617425721106…97854234057323939839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.930 Γ— 10⁹⁷(98-digit number)
39301711234851442212…95708468114647879679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.860 Γ— 10⁹⁷(98-digit number)
78603422469702884425…91416936229295759359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.572 Γ— 10⁹⁸(99-digit number)
15720684493940576885…82833872458591518719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.144 Γ— 10⁹⁸(99-digit number)
31441368987881153770…65667744917183037439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.288 Γ— 10⁹⁸(99-digit number)
62882737975762307540…31335489834366074879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.257 Γ— 10⁹⁹(100-digit number)
12576547595152461508…62670979668732149759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.515 Γ— 10⁹⁹(100-digit number)
25153095190304923016…25341959337464299519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.030 Γ— 10⁹⁹(100-digit number)
50306190380609846032…50683918674928599039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.006 Γ— 10¹⁰⁰(101-digit number)
10061238076121969206…01367837349857198079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.012 Γ— 10¹⁰⁰(101-digit number)
20122476152243938412…02735674699714396159
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 663042

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 41f78d83449d78c9139a2aae72f9c8259e3662a0f9a354797dfa8d3c0d00c4ba

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 #663,042 on Chainz β†—
Circulating Supply:57,614,687 XPMΒ·at block #6,796,336 Β· updates every 60s
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