Block #483,501

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/10/2014, 2:24:38 AM · Difficulty 10.5635 · 6,319,816 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
331995276f2a4640bb8568ec4c6de66ba6f3b16c3f6042323b5c5ddb4b873553

Height

#483,501

Difficulty

10.563527

Transactions

2

Size

595 B

Version

2

Bits

0a904351

Nonce

1,720

Timestamp

4/10/2014, 2:24:38 AM

Confirmations

6,319,816

Merkle Root

c628898b3d2385c69578532a08a81ca56f50e64273f841b0f8801303dc2f150b
Transactions (2)
1 in → 1 out8.9600 XPM116 B
3 in → 1 out27.1700 XPM387 B
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.

2.026 × 10⁹⁹(100-digit number)
20263383586642100440…03034004985493534719
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
2.026 × 10⁹⁹(100-digit number)
20263383586642100440…03034004985493534719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.052 × 10⁹⁹(100-digit number)
40526767173284200881…06068009970987069439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
8.105 × 10⁹⁹(100-digit number)
81053534346568401763…12136019941974138879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.621 × 10¹⁰⁰(101-digit number)
16210706869313680352…24272039883948277759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.242 × 10¹⁰⁰(101-digit number)
32421413738627360705…48544079767896555519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
6.484 × 10¹⁰⁰(101-digit number)
64842827477254721410…97088159535793111039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.296 × 10¹⁰¹(102-digit number)
12968565495450944282…94176319071586222079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.593 × 10¹⁰¹(102-digit number)
25937130990901888564…88352638143172444159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.187 × 10¹⁰¹(102-digit number)
51874261981803777128…76705276286344888319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.037 × 10¹⁰²(103-digit number)
10374852396360755425…53410552572689776639
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:57,670,565 XPM·at block #6,803,316 · updates every 60s
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