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Block #2,767,988

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/27/2018, 7:56:01 PM Β· Difficulty 11.6668 Β· 4,076,514 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
da794984520c2f8ab6cc2a4243bc11c53f487c83c7bae23ceb36279db390e961
View on Chainz β†—

Height

#2,767,988

Difficulty

11.666807

Transactions

1

Size

199 B

Version

2

Bits

0baab3d5

Nonce

1,727,473,299

Timestamp

7/27/2018, 7:56:01 PM

Confirmations

4,076,514

Mined by

⛏️ P2SHALCKwEoSScaCifty2vqQzz7PuLBynYXTir

Merkle Root

9b817e01c824005cd832ba7fccb054f96b759dbae77bc8d8ab23c34d78c312c6
Transactions (1)
Coinbase9b817e01c82400…23c34d78c312c6
1 in β†’ 1 out7.3300 XPM109 B
ALCKwEoS…BynYXTir
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.

1.170 Γ— 10⁹⁴(95-digit number)
11706864120515151222…15276594658274734719
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
1.170 Γ— 10⁹⁴(95-digit number)
11706864120515151222…15276594658274734719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.341 Γ— 10⁹⁴(95-digit number)
23413728241030302444…30553189316549469439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.682 Γ— 10⁹⁴(95-digit number)
46827456482060604889…61106378633098938879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.365 Γ— 10⁹⁴(95-digit number)
93654912964121209779…22212757266197877759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.873 Γ— 10⁹⁡(96-digit number)
18730982592824241955…44425514532395755519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.746 Γ— 10⁹⁡(96-digit number)
37461965185648483911…88851029064791511039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.492 Γ— 10⁹⁡(96-digit number)
74923930371296967823…77702058129583022079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.498 Γ— 10⁹⁢(97-digit number)
14984786074259393564…55404116259166044159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.996 Γ— 10⁹⁢(97-digit number)
29969572148518787129…10808232518332088319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.993 Γ— 10⁹⁢(97-digit number)
59939144297037574258…21616465036664176639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.198 Γ— 10⁹⁷(98-digit number)
11987828859407514851…43232930073328353279
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:58,000,413 XPMΒ·at block #6,844,501 Β· updates every 60s
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