Block #976,498

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 3/16/2015, 4:01:47 AM · Difficulty 10.8473 · 5,830,582 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
58107f0a7b261a4319aef6a2ad56a865dd6915cd1737b0d7eef48563e378205a

Height

#976,498

Difficulty

10.847266

Transactions

2

Size

727 B

Version

2

Bits

0ad8e66b

Nonce

60,543,947

Timestamp

3/16/2015, 4:01:47 AM

Confirmations

5,830,582

Merkle Root

87c6d023c989555648722d5568f75e804ed799193d1cb9b6c2df8b57fb3c5948
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.

1.768 × 10⁹⁸(99-digit number)
17688914078800588087…20793654752071700479
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
1.768 × 10⁹⁸(99-digit number)
17688914078800588087…20793654752071700479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.537 × 10⁹⁸(99-digit number)
35377828157601176174…41587309504143400959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
7.075 × 10⁹⁸(99-digit number)
70755656315202352348…83174619008286801919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.415 × 10⁹⁹(100-digit number)
14151131263040470469…66349238016573603839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.830 × 10⁹⁹(100-digit number)
28302262526080940939…32698476033147207679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
5.660 × 10⁹⁹(100-digit number)
56604525052161881878…65396952066294415359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.132 × 10¹⁰⁰(101-digit number)
11320905010432376375…30793904132588830719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.264 × 10¹⁰⁰(101-digit number)
22641810020864752751…61587808265177661439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.528 × 10¹⁰⁰(101-digit number)
45283620041729505503…23175616530355322879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
9.056 × 10¹⁰⁰(101-digit number)
90567240083459011006…46351233060710645759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.811 × 10¹⁰¹(102-digit number)
18113448016691802201…92702466121421291519
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:57,700,736 XPM·at block #6,807,079 · updates every 60s
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