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Block #2,685,655

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 5/31/2018, 9:25:10 AM Β· Difficulty 11.6884 Β· 4,151,008 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
22f7c539672fe8afba87fd179ea94decd250e8ff49737953f4fe91674b539d14
View on Chainz β†—

Height

#2,685,655

Difficulty

11.688409

Transactions

2

Size

1018 B

Version

2

Bits

0bb03b8b

Nonce

173,467,071

Timestamp

5/31/2018, 9:25:10 AM

Confirmations

4,151,008

Mined by

⛏️ P2SHALmZeLw23bph3FA1jhy6VNqoyGnvcacpSB

Merkle Root

650f55869b4333081ac3def1e337b826562c37683dc7a98a6f08669f39221652
Transactions (2)
Coinbasefd7f871be4f7b6…bd4ca91895ad5d
1 in β†’ 1 out7.3200 XPM110 B
ALmZeLw2…nvcacpSB
b2f0b47377effc…8a77eb6b43cddf
5 in β†’ 2 out9642.8900 XPM818 B
AHQy4zE5…fjwXyK3nAU9Uf3mu…6myV9DkT
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.

2.876 Γ— 10⁹⁴(95-digit number)
28761260106472947411…24232647198640459079
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
2.876 Γ— 10⁹⁴(95-digit number)
28761260106472947411…24232647198640459079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.752 Γ— 10⁹⁴(95-digit number)
57522520212945894822…48465294397280918159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.150 Γ— 10⁹⁡(96-digit number)
11504504042589178964…96930588794561836319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.300 Γ— 10⁹⁡(96-digit number)
23009008085178357929…93861177589123672639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.601 Γ— 10⁹⁡(96-digit number)
46018016170356715858…87722355178247345279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.203 Γ— 10⁹⁡(96-digit number)
92036032340713431716…75444710356494690559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.840 Γ— 10⁹⁢(97-digit number)
18407206468142686343…50889420712989381119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.681 Γ— 10⁹⁢(97-digit number)
36814412936285372686…01778841425978762239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.362 Γ— 10⁹⁢(97-digit number)
73628825872570745373…03557682851957524479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.472 Γ— 10⁹⁷(98-digit number)
14725765174514149074…07115365703915048959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.945 Γ— 10⁹⁷(98-digit number)
29451530349028298149…14230731407830097919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
5.890 Γ— 10⁹⁷(98-digit number)
58903060698056596298…28461462815660195839
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,937,581 XPMΒ·at block #6,836,662 Β· updates every 60s
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