Block #1,228,600

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 9/9/2015, 9:36:51 AM · Difficulty 10.7341 · 5,577,411 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a918aec5f88e999b08c8024b0968f6a6f2e8f11a83ef089d94a43999c7a07267

Height

#1,228,600

Difficulty

10.734145

Transactions

3

Size

945 B

Version

2

Bits

0abbf0f2

Nonce

348,818,719

Timestamp

9/9/2015, 9:36:51 AM

Confirmations

5,577,411

Merkle Root

fc501831de8e2c1139df7bbe93b7666dce1065afa6655a04e1663d6e239a3f6a
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.

2.663 × 10⁹⁴(95-digit number)
26639663601417126328…22392084863757593599
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
2.663 × 10⁹⁴(95-digit number)
26639663601417126328…22392084863757593599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
5.327 × 10⁹⁴(95-digit number)
53279327202834252656…44784169727515187199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.065 × 10⁹⁵(96-digit number)
10655865440566850531…89568339455030374399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.131 × 10⁹⁵(96-digit number)
21311730881133701062…79136678910060748799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
4.262 × 10⁹⁵(96-digit number)
42623461762267402125…58273357820121497599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
8.524 × 10⁹⁵(96-digit number)
85246923524534804251…16546715640242995199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.704 × 10⁹⁶(97-digit number)
17049384704906960850…33093431280485990399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.409 × 10⁹⁶(97-digit number)
34098769409813921700…66186862560971980799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
6.819 × 10⁹⁶(97-digit number)
68197538819627843400…32373725121943961599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.363 × 10⁹⁷(98-digit number)
13639507763925568680…64747450243887923199
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,692,166 XPM·at block #6,806,010 · updates every 60s
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