Block #2,655,615

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 5/10/2018, 8:09:30 AM · Difficulty 11.7040 · 4,185,508 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a36ba079e91d38080f26584f642932eed3cfd666b3ee3ad3a58205cffe2af387

Height

#2,655,615

Difficulty

11.704004

Transactions

2

Size

1018 B

Version

2

Bits

0bb439a1

Nonce

1,196,989,046

Timestamp

5/10/2018, 8:09:30 AM

Confirmations

4,185,508

Merkle Root

dd107d324daec244d0219e696010c61e7baa51c1564457ec22a92a69378e761d
Transactions (2)
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

4.383 × 10⁹⁵(96-digit number)
43838833467999446888…68602581589044792759
Discovered Prime Numbers
p_k = 2^k × origin − 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 − 1
4.383 × 10⁹⁵(96-digit number)
43838833467999446888…68602581589044792759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
8.767 × 10⁹⁵(96-digit number)
87677666935998893776…37205163178089585519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.753 × 10⁹⁶(97-digit number)
17535533387199778755…74410326356179171039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.507 × 10⁹⁶(97-digit number)
35071066774399557510…48820652712358342079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
7.014 × 10⁹⁶(97-digit number)
70142133548799115021…97641305424716684159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.402 × 10⁹⁷(98-digit number)
14028426709759823004…95282610849433368319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.805 × 10⁹⁷(98-digit number)
28056853419519646008…90565221698866736639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
5.611 × 10⁹⁷(98-digit number)
56113706839039292017…81130443397733473279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.122 × 10⁹⁸(99-digit number)
11222741367807858403…62260886795466946559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.244 × 10⁹⁸(99-digit number)
22445482735615716806…24521773590933893119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
4.489 × 10⁹⁸(99-digit number)
44890965471231433613…49043547181867786239
Verify on FactorDB ↗Wolfram Alpha ↗

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★★☆☆
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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)
Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,973,353 XPM·at block #6,841,122 · updates every 60s
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