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Block #2,635,593

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/29/2018, 7:20:03 AM Β· Difficulty 11.3265 Β· 4,202,189 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
86d59443ff8973e7b533c74d6ebc40bbeddf092732157c0810504393ae68c5fa
View on Chainz β†—

Height

#2,635,593

Difficulty

11.326540

Transactions

1

Size

201 B

Version

2

Bits

0b539825

Nonce

279,764,340

Timestamp

4/29/2018, 7:20:03 AM

Confirmations

4,202,189

Mined by

⛏️ P2SHAGgp4bLnnqSFGuYHeox5NtrrAJKjU1x1Rj

Merkle Root

ffaa53385ae7ed1426f4c40013a2b836c8f8c048b49dd3e7799b9feabcee5efe
Transactions (1)
Coinbaseffaa53385ae7ed…9b9feabcee5efe
1 in β†’ 1 out7.7800 XPM110 B
AGgp4bLn…KjU1x1Rj
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.

1.262 Γ— 10⁹⁷(98-digit number)
12624157051352765302…15780396038460948479
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
1.262 Γ— 10⁹⁷(98-digit number)
12624157051352765302…15780396038460948479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.524 Γ— 10⁹⁷(98-digit number)
25248314102705530604…31560792076921896959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.049 Γ— 10⁹⁷(98-digit number)
50496628205411061209…63121584153843793919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.009 Γ— 10⁹⁸(99-digit number)
10099325641082212241…26243168307687587839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.019 Γ— 10⁹⁸(99-digit number)
20198651282164424483…52486336615375175679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.039 Γ— 10⁹⁸(99-digit number)
40397302564328848967…04972673230750351359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.079 Γ— 10⁹⁸(99-digit number)
80794605128657697934…09945346461500702719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.615 Γ— 10⁹⁹(100-digit number)
16158921025731539586…19890692923001405439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.231 Γ— 10⁹⁹(100-digit number)
32317842051463079173…39781385846002810879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.463 Γ— 10⁹⁹(100-digit number)
64635684102926158347…79562771692005621759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.292 Γ— 10¹⁰⁰(101-digit number)
12927136820585231669…59125543384011243519
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:57,946,593 XPMΒ·at block #6,837,781 Β· updates every 60s
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