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Block #2,670,640

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/20/2018, 11:56:26 PM Β· Difficulty 11.6850 Β· 4,160,658 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e5ad4548878d827d237aa45243fc3f9e3cfcfc2368df7b4cf9e4808e2e5dc3e6
View on Chainz β†—

Height

#2,670,640

Difficulty

11.684987

Transactions

2

Size

575 B

Version

2

Bits

0baf5b51

Nonce

640,719,434

Timestamp

5/20/2018, 11:56:26 PM

Confirmations

4,160,658

Mined by

⛏️ P2SHAMvUeCghZYu7Rj99fMcqdC3nnZAMrztCFU

Merkle Root

303aff5b40a14abeca16f53e041ef1485c45373c1769515acb3274a33c4a81b3
Transactions (2)
Coinbased4e71cb26123f6…a8fd429f34fc73
1 in β†’ 1 out7.3200 XPM110 B
AMvUeCgh…AMrztCFU
2959b5030acaa8…83784df8df32e3
2 in β†’ 2 out105.7177 XPM375 B
AUiqU7GG…9DQRn1rVAaTN4273…RTonuvf3
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.

8.792 Γ— 10⁹⁴(95-digit number)
87925956706532438864…29496673151472827119
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
8.792 Γ— 10⁹⁴(95-digit number)
87925956706532438864…29496673151472827119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.758 Γ— 10⁹⁡(96-digit number)
17585191341306487772…58993346302945654239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.517 Γ— 10⁹⁡(96-digit number)
35170382682612975545…17986692605891308479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.034 Γ— 10⁹⁡(96-digit number)
70340765365225951091…35973385211782616959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.406 Γ— 10⁹⁢(97-digit number)
14068153073045190218…71946770423565233919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.813 Γ— 10⁹⁢(97-digit number)
28136306146090380436…43893540847130467839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.627 Γ— 10⁹⁢(97-digit number)
56272612292180760873…87787081694260935679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.125 Γ— 10⁹⁷(98-digit number)
11254522458436152174…75574163388521871359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.250 Γ— 10⁹⁷(98-digit number)
22509044916872304349…51148326777043742719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.501 Γ— 10⁹⁷(98-digit number)
45018089833744608698…02296653554087485439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.003 Γ— 10⁹⁷(98-digit number)
90036179667489217396…04593307108174970879
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:57,894,531 XPMΒ·at block #6,831,297 Β· updates every 60s
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