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Block #2,847,431

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 9/20/2018, 6:04:50 AM Β· Difficulty 11.7331 Β· 3,989,450 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
445118598acc08562b31948d579b3b7df41369e1a29fe5c425d1423507f2f543
View on Chainz β†—

Height

#2,847,431

Difficulty

11.733092

Transactions

1

Size

200 B

Version

2

Bits

0bbbabf1

Nonce

1,357,156,731

Timestamp

9/20/2018, 6:04:50 AM

Confirmations

3,989,450

Mined by

⛏️ P2SHAWkzuRQuSEmL8GHmsoxMDJnNvpNqxNpVgv

Merkle Root

742481d22389d8520fa105e6a2bec85c136b0cb8d0caca0ba72cdc34b961a4ff
Transactions (1)
Coinbase742481d22389d8…2cdc34b961a4ff
1 in β†’ 1 out7.2500 XPM110 B
AWkzuRQu…NqxNpVgv
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.

7.188 Γ— 10⁹³(94-digit number)
71884828629088799646…89462014893413699019
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
7.188 Γ— 10⁹³(94-digit number)
71884828629088799646…89462014893413699019
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.437 Γ— 10⁹⁴(95-digit number)
14376965725817759929…78924029786827398039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.875 Γ— 10⁹⁴(95-digit number)
28753931451635519858…57848059573654796079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.750 Γ— 10⁹⁴(95-digit number)
57507862903271039717…15696119147309592159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.150 Γ— 10⁹⁡(96-digit number)
11501572580654207943…31392238294619184319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.300 Γ— 10⁹⁡(96-digit number)
23003145161308415886…62784476589238368639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.600 Γ— 10⁹⁡(96-digit number)
46006290322616831773…25568953178476737279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.201 Γ— 10⁹⁡(96-digit number)
92012580645233663547…51137906356953474559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.840 Γ— 10⁹⁢(97-digit number)
18402516129046732709…02275812713906949119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.680 Γ— 10⁹⁢(97-digit number)
36805032258093465419…04551625427813898239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.361 Γ— 10⁹⁢(97-digit number)
73610064516186930838…09103250855627796479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
1.472 Γ— 10⁹⁷(98-digit number)
14722012903237386167…18206501711255592959
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:57,939,339 XPMΒ·at block #6,836,880 Β· updates every 60s
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