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Block #2,634,886

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/29/2018, 1:31:57 AM Β· Difficulty 11.2769 Β· 4,209,586 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8696cafaac95bde24ba181f4059426a365176e2031d87bd28a309e09392634ab
View on Chainz β†—

Height

#2,634,886

Difficulty

11.276931

Transactions

1

Size

200 B

Version

2

Bits

0b46e4ee

Nonce

1,965,994,983

Timestamp

4/29/2018, 1:31:57 AM

Confirmations

4,209,586

Mined by

⛏️ P2SHAcPEpnQQaDD4BpSU2BLZMUz9exLysTjs6r

Merkle Root

ddfdbfb32b5c0632f8dc876e092ed1fcf8977d0e189e7df584529fdf02563bf4
Transactions (1)
Coinbaseddfdbfb32b5c06…529fdf02563bf4
1 in β†’ 1 out7.8500 XPM110 B
AcPEpnQQ…LysTjs6r
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.

4.475 Γ— 10⁹³(94-digit number)
44757435769473170726…84912606453398905359
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
4.475 Γ— 10⁹³(94-digit number)
44757435769473170726…84912606453398905359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.951 Γ— 10⁹³(94-digit number)
89514871538946341452…69825212906797810719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.790 Γ— 10⁹⁴(95-digit number)
17902974307789268290…39650425813595621439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.580 Γ— 10⁹⁴(95-digit number)
35805948615578536581…79300851627191242879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.161 Γ— 10⁹⁴(95-digit number)
71611897231157073162…58601703254382485759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.432 Γ— 10⁹⁡(96-digit number)
14322379446231414632…17203406508764971519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.864 Γ— 10⁹⁡(96-digit number)
28644758892462829264…34406813017529943039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.728 Γ— 10⁹⁡(96-digit number)
57289517784925658529…68813626035059886079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.145 Γ— 10⁹⁢(97-digit number)
11457903556985131705…37627252070119772159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.291 Γ— 10⁹⁢(97-digit number)
22915807113970263411…75254504140239544319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.583 Γ— 10⁹⁢(97-digit number)
45831614227940526823…50509008280479088639
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:58,000,171 XPMΒ·at block #6,844,471 Β· updates every 60s
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