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Block #663,748

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/5/2014, 12:14:25 PM Β· Difficulty 10.9577 Β· 6,163,388 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
bc3497a30e404094d685f59274098aa5ffdcd4c25611ba6a5867663b0a5db165
View on Chainz β†—

Height

#663,748

Difficulty

10.957695

Transactions

2

Size

364 B

Version

2

Bits

0af52b81

Nonce

105,200,486

Timestamp

8/5/2014, 12:14:25 PM

Confirmations

6,163,388

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

dd25ce1ca0194aaf625bbce312e698bd4db23ef4b74588d5f64a64ec84ba88e3
Transactions (2)
Coinbasea704b46002a0e3…dc7edc39fec1e7
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
a025d576da11c7…240ae419878cee
1 in β†’ 1 out8.9200 XPM157 B
AR7n9chB…ozyWpotN
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.

1.273 Γ— 10⁹⁸(99-digit number)
12736867199024754435…64503949459280575999
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
1.273 Γ— 10⁹⁸(99-digit number)
12736867199024754435…64503949459280575999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.547 Γ— 10⁹⁸(99-digit number)
25473734398049508870…29007898918561151999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.094 Γ— 10⁹⁸(99-digit number)
50947468796099017740…58015797837122303999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.018 Γ— 10⁹⁹(100-digit number)
10189493759219803548…16031595674244607999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.037 Γ— 10⁹⁹(100-digit number)
20378987518439607096…32063191348489215999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.075 Γ— 10⁹⁹(100-digit number)
40757975036879214192…64126382696978431999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.151 Γ— 10⁹⁹(100-digit number)
81515950073758428384…28252765393956863999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.630 Γ— 10¹⁰⁰(101-digit number)
16303190014751685676…56505530787913727999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.260 Γ— 10¹⁰⁰(101-digit number)
32606380029503371353…13011061575827455999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.521 Γ— 10¹⁰⁰(101-digit number)
65212760059006742707…26022123151654911999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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.

β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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, …
Cross-reference on Chainz Explorer
Circulating Supply:57,861,269 XPMΒ·at block #6,827,135 Β· updates every 60s
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