Block #1,280,404

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 10/13/2015, 4:20:57 PM · Difficulty 10.8374 · 5,529,454 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
60a4ef1983be9fea2bdc75085263bec80c9e2f0ef2ca3b04af16ca4a86675a42

Height

#1,280,404

Difficulty

10.837434

Transactions

3

Size

651 B

Version

2

Bits

0ad6620d

Nonce

211,277,399

Timestamp

10/13/2015, 4:20:57 PM

Confirmations

5,529,454

Merkle Root

2f605ebe3af233e353ffd9bcb3b0115d9ce41d1ad4b88130412a4a85809fd89c
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.

9.895 × 10⁹⁴(95-digit number)
98950867437846623462…84726893684368415039
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
9.895 × 10⁹⁴(95-digit number)
98950867437846623462…84726893684368415039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.979 × 10⁹⁵(96-digit number)
19790173487569324692…69453787368736830079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.958 × 10⁹⁵(96-digit number)
39580346975138649384…38907574737473660159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.916 × 10⁹⁵(96-digit number)
79160693950277298769…77815149474947320319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.583 × 10⁹⁶(97-digit number)
15832138790055459753…55630298949894640639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.166 × 10⁹⁶(97-digit number)
31664277580110919507…11260597899789281279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
6.332 × 10⁹⁶(97-digit number)
63328555160221839015…22521195799578562559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.266 × 10⁹⁷(98-digit number)
12665711032044367803…45042391599157125119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.533 × 10⁹⁷(98-digit number)
25331422064088735606…90084783198314250239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
5.066 × 10⁹⁷(98-digit number)
50662844128177471212…80169566396628500479
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:57,722,952 XPM·at block #6,809,857 · updates every 60s
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