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Block #2,634,396

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/28/2018, 9:13:09 PM Β· Difficulty 11.2428 Β· 4,196,499 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
83e5aa936edec773a7b79798dfba49473df3a17eacd871c1f8122e31dc4c7822
View on Chainz β†—

Height

#2,634,396

Difficulty

11.242839

Transactions

1

Size

200 B

Version

2

Bits

0b3e2aaf

Nonce

1,901,886,436

Timestamp

4/28/2018, 9:13:09 PM

Confirmations

4,196,499

Mined by

⛏️ P2SHAMqG4ciDCuP41s4eao48KMKBLmyzYKpRhF

Merkle Root

6b85d8d6a307168238c14dc41fd4154dfe95aecfa02f5a5fb38077d0dbbeec01
Transactions (1)
Coinbase6b85d8d6a30716…8077d0dbbeec01
1 in β†’ 1 out7.9000 XPM109 B
AMqG4ciD…yzYKpRhF
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.

3.963 Γ— 10⁹⁢(97-digit number)
39633305856609241450…87417511633714544639
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
3.963 Γ— 10⁹⁢(97-digit number)
39633305856609241450…87417511633714544639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.926 Γ— 10⁹⁢(97-digit number)
79266611713218482900…74835023267429089279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.585 Γ— 10⁹⁷(98-digit number)
15853322342643696580…49670046534858178559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.170 Γ— 10⁹⁷(98-digit number)
31706644685287393160…99340093069716357119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.341 Γ— 10⁹⁷(98-digit number)
63413289370574786320…98680186139432714239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.268 Γ— 10⁹⁸(99-digit number)
12682657874114957264…97360372278865428479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.536 Γ— 10⁹⁸(99-digit number)
25365315748229914528…94720744557730856959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.073 Γ— 10⁹⁸(99-digit number)
50730631496459829056…89441489115461713919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.014 Γ— 10⁹⁹(100-digit number)
10146126299291965811…78882978230923427839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.029 Γ— 10⁹⁹(100-digit number)
20292252598583931622…57765956461846855679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.058 Γ— 10⁹⁹(100-digit number)
40584505197167863244…15531912923693711359
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:57,891,287 XPMΒ·at block #6,830,894 Β· updates every 60s
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