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Block #2,622,167

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/20/2018, 10:29:00 AM Β· Difficulty 11.2327 Β· 4,214,815 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f14a709791cd35832ad9dfe475559765d8e93cabc189e6d1f322f039fbcb289d
View on Chainz β†—

Height

#2,622,167

Difficulty

11.232746

Transactions

2

Size

6.75 KB

Version

2

Bits

0b3b9539

Nonce

30,498,192

Timestamp

4/20/2018, 10:29:00 AM

Confirmations

4,214,815

Mined by

⛏️ P2SHAcAK625uuqm5gyB67PhdSSDX7h8V1gw11A

Merkle Root

cde1ae1803c8ba661043eb19780defc1292c8d0fc68416e74b6b422f64a4c894
Transactions (2)
Coinbasef4fd31bd848a05…324312921f5b3f
1 in β†’ 1 out7.9800 XPM109 B
AcAK625u…8V1gw11A
1c1a9fa465c5e1…214da77ef63ef8
45 in β†’ 2 out500.5906 XPM6.56 KB
AcwTzPwJ…LKXSapvyAMgtSW8g…rQ2J57yA
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.

2.113 Γ— 10⁹⁢(97-digit number)
21138347048783192261…11249824553750609919
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
2.113 Γ— 10⁹⁢(97-digit number)
21138347048783192261…11249824553750609919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.227 Γ— 10⁹⁢(97-digit number)
42276694097566384523…22499649107501219839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.455 Γ— 10⁹⁢(97-digit number)
84553388195132769047…44999298215002439679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.691 Γ— 10⁹⁷(98-digit number)
16910677639026553809…89998596430004879359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.382 Γ— 10⁹⁷(98-digit number)
33821355278053107618…79997192860009758719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.764 Γ— 10⁹⁷(98-digit number)
67642710556106215237…59994385720019517439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.352 Γ— 10⁹⁸(99-digit number)
13528542111221243047…19988771440039034879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.705 Γ— 10⁹⁸(99-digit number)
27057084222442486095…39977542880078069759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.411 Γ— 10⁹⁸(99-digit number)
54114168444884972190…79955085760156139519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.082 Γ— 10⁹⁹(100-digit number)
10822833688976994438…59910171520312279039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.164 Γ— 10⁹⁹(100-digit number)
21645667377953988876…19820343040624558079
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:57,940,155 XPMΒ·at block #6,836,981 Β· updates every 60s
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