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Block #1,402,264

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/7/2016, 12:17:42 AM Β· Difficulty 10.8062 Β· 5,410,177 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
63d84200f1f2686f8ffa2346449385a30b9e8e93ad71e44fee9b802d9754bc96
View on Chainz β†—

Height

#1,402,264

Difficulty

10.806150

Transactions

2

Size

1.72 KB

Version

2

Bits

0ace5fdf

Nonce

1,424,482,237

Timestamp

1/7/2016, 12:17:42 AM

Confirmations

5,410,177

Mined by

⛏️ P2SHAL4yWViguBTp21AexpPnH55TA5RhioqMCv

Merkle Root

db705e5e2a6b12196ec32113a7338829ee0a6db4672ffd57f7bcc93f888dea7d
Transactions (2)
Coinbase2fb5a462280830…428616d4806ce6
1 in β†’ 1 out8.5700 XPM110 B
AL4yWVig…RhioqMCv
04931f144a4555…d5c3b98dd043a2
10 in β†’ 2 out89.5112 XPM1.52 KB
AbecWDS9…1vtToSMLAH5b1wVp…NHMyA6BK
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.

8.416 Γ— 10⁹⁡(96-digit number)
84161305856882943294…58804791334754682879
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
8.416 Γ— 10⁹⁡(96-digit number)
84161305856882943294…58804791334754682879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.683 Γ— 10⁹⁢(97-digit number)
16832261171376588658…17609582669509365759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.366 Γ— 10⁹⁢(97-digit number)
33664522342753177317…35219165339018731519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.732 Γ— 10⁹⁢(97-digit number)
67329044685506354635…70438330678037463039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.346 Γ— 10⁹⁷(98-digit number)
13465808937101270927…40876661356074926079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.693 Γ— 10⁹⁷(98-digit number)
26931617874202541854…81753322712149852159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.386 Γ— 10⁹⁷(98-digit number)
53863235748405083708…63506645424299704319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.077 Γ— 10⁹⁸(99-digit number)
10772647149681016741…27013290848599408639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.154 Γ— 10⁹⁸(99-digit number)
21545294299362033483…54026581697198817279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.309 Γ— 10⁹⁸(99-digit number)
43090588598724066966…08053163394397634559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
8.618 Γ— 10⁹⁸(99-digit number)
86181177197448133933…16106326788795269119
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.

β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,743,550 XPMΒ·at block #6,812,440 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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