Block #973,321

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 3/14/2015, 1:01:01 AM · Difficulty 10.8436 · 5,841,535 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ddb7bad178dfe2096653c60183aa56f11ba5d89b7662c58a67d4151b5f8ce530

Height

#973,321

Difficulty

10.843605

Transactions

2

Size

876 B

Version

2

Bits

0ad7f685

Nonce

2,434,574,861

Timestamp

3/14/2015, 1:01:01 AM

Confirmations

5,841,535

Merkle Root

21f17187fadf219828d5af070b06df8d7738eb18cd90222dcd2e7a5edd6ed97b
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.

5.810 × 10⁹⁷(98-digit number)
58102533864864647655…78742779550354739199
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
5.810 × 10⁹⁷(98-digit number)
58102533864864647655…78742779550354739199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.162 × 10⁹⁸(99-digit number)
11620506772972929531…57485559100709478399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.324 × 10⁹⁸(99-digit number)
23241013545945859062…14971118201418956799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.648 × 10⁹⁸(99-digit number)
46482027091891718124…29942236402837913599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
9.296 × 10⁹⁸(99-digit number)
92964054183783436249…59884472805675827199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.859 × 10⁹⁹(100-digit number)
18592810836756687249…19768945611351654399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.718 × 10⁹⁹(100-digit number)
37185621673513374499…39537891222703308799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
7.437 × 10⁹⁹(100-digit number)
74371243347026748999…79075782445406617599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.487 × 10¹⁰⁰(101-digit number)
14874248669405349799…58151564890813235199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.974 × 10¹⁰⁰(101-digit number)
29748497338810699599…16303129781626470399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
5.949 × 10¹⁰⁰(101-digit number)
59496994677621399199…32606259563252940799
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:57,762,932 XPM·at block #6,814,855 · updates every 60s
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