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Block #2,772,858

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/31/2018, 6:12:18 AM Β· Difficulty 11.6626 Β· 4,070,139 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
421646050405b1b96b4097492e89020c491c729805c5b711314d0c4937d23517
View on Chainz β†—

Height

#2,772,858

Difficulty

11.662572

Transactions

1

Size

200 B

Version

2

Bits

0ba99e59

Nonce

1,855,748,351

Timestamp

7/31/2018, 6:12:18 AM

Confirmations

4,070,139

Mined by

⛏️ P2SHAcQXGPUzUJaai1wNz3gka4GoUoXbQp9Xsa

Merkle Root

6c81678fd9cbccb0d73e0fd04c60c7303cce921aaaa54c4ba58499d7a5d6397e
Transactions (1)
Coinbase6c81678fd9cbcc…8499d7a5d6397e
1 in β†’ 1 out7.3400 XPM110 B
AcQXGPUz…XbQp9Xsa
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.

5.735 Γ— 10⁹⁴(95-digit number)
57354484057358608239…69343549477787048959
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
5.735 Γ— 10⁹⁴(95-digit number)
57354484057358608239…69343549477787048959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.147 Γ— 10⁹⁡(96-digit number)
11470896811471721647…38687098955574097919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.294 Γ— 10⁹⁡(96-digit number)
22941793622943443295…77374197911148195839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.588 Γ— 10⁹⁡(96-digit number)
45883587245886886591…54748395822296391679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.176 Γ— 10⁹⁡(96-digit number)
91767174491773773182…09496791644592783359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.835 Γ— 10⁹⁢(97-digit number)
18353434898354754636…18993583289185566719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.670 Γ— 10⁹⁢(97-digit number)
36706869796709509273…37987166578371133439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.341 Γ— 10⁹⁢(97-digit number)
73413739593419018546…75974333156742266879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.468 Γ— 10⁹⁷(98-digit number)
14682747918683803709…51948666313484533759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.936 Γ— 10⁹⁷(98-digit number)
29365495837367607418…03897332626969067519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.873 Γ— 10⁹⁷(98-digit number)
58730991674735214837…07794665253938135039
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:57,988,331 XPMΒ·at block #6,842,996 Β· updates every 60s
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