1. #6,817,0952CC10 primes

    Cunningham 2nd · ⛏️ coinsforall.io

Block #466,464

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 3/30/2014, 4:56:08 AM · Difficulty 10.4211 · 6,350,632 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ccb2d98d5af3af74441cd5a6a622df7139b68fbd316e5bcf4f7597e2c1f81ba1

Height

#466,464

Difficulty

10.421066

Transactions

1

Size

935 B

Version

2

Bits

0a6bcb00

Nonce

23,452

Timestamp

3/30/2014, 4:56:08 AM

Confirmations

6,350,632

Merkle Root

c1410647ca0344c62b06ffe6b3a4de272e50e53a969522f4dcc251a3bc201fb7
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.

5.618 × 10⁹³(94-digit number)
56188038869594013668…86728652193013601439
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
5.618 × 10⁹³(94-digit number)
56188038869594013668…86728652193013601439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.123 × 10⁹⁴(95-digit number)
11237607773918802733…73457304386027202879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.247 × 10⁹⁴(95-digit number)
22475215547837605467…46914608772054405759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.495 × 10⁹⁴(95-digit number)
44950431095675210934…93829217544108811519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
8.990 × 10⁹⁴(95-digit number)
89900862191350421869…87658435088217623039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.798 × 10⁹⁵(96-digit number)
17980172438270084373…75316870176435246079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.596 × 10⁹⁵(96-digit number)
35960344876540168747…50633740352870492159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
7.192 × 10⁹⁵(96-digit number)
71920689753080337495…01267480705740984319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.438 × 10⁹⁶(97-digit number)
14384137950616067499…02534961411481968639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.876 × 10⁹⁶(97-digit number)
28768275901232134998…05069922822963937279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
5.753 × 10⁹⁶(97-digit number)
57536551802464269996…10139845645927874559
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:57,780,805 XPM·at block #6,817,095 · updates every 60s
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