Block #1,372,600

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/17/2015, 8:06:40 AM · Difficulty 10.8093 · 5,454,362 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3a8a63b7793df719daa45eb507599014b9231f7b1b0ca816b1636486d13e2ed9

Height

#1,372,600

Difficulty

10.809303

Transactions

2

Size

1.15 KB

Version

2

Bits

0acf2e73

Nonce

966,715,486

Timestamp

12/17/2015, 8:06:40 AM

Confirmations

5,454,362

Merkle Root

44b715d483c0d6f6ea31a97332b0c06e3e906a28b503dbbd340865828c0d10d5
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.

1.124 × 10⁹⁶(97-digit number)
11242122303328380562…07137740643999528959
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
1.124 × 10⁹⁶(97-digit number)
11242122303328380562…07137740643999528959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.248 × 10⁹⁶(97-digit number)
22484244606656761125…14275481287999057919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.496 × 10⁹⁶(97-digit number)
44968489213313522250…28550962575998115839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
8.993 × 10⁹⁶(97-digit number)
89936978426627044501…57101925151996231679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.798 × 10⁹⁷(98-digit number)
17987395685325408900…14203850303992463359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.597 × 10⁹⁷(98-digit number)
35974791370650817800…28407700607984926719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
7.194 × 10⁹⁷(98-digit number)
71949582741301635601…56815401215969853439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.438 × 10⁹⁸(99-digit number)
14389916548260327120…13630802431939706879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.877 × 10⁹⁸(99-digit number)
28779833096520654240…27261604863879413759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
5.755 × 10⁹⁸(99-digit number)
57559666193041308480…54523209727758827519
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:57,859,872 XPM·at block #6,826,961 · updates every 60s
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