1. #6,810,353TWN11 primes

    Bi-Twin · ⛏️ coinsforall.io

Block #485,350

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/11/2014, 12:24:51 AM · Difficulty 10.6070 · 6,325,004 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b98c127c0de9d51cf12b183557acb802958361618cbc989aa7dcb79c4e0ee2fa

Height

#485,350

Difficulty

10.606971

Transactions

5

Size

3.26 KB

Version

2

Bits

0a9b626e

Nonce

685,904,226

Timestamp

4/11/2014, 12:24:51 AM

Confirmations

6,325,004

Merkle Root

17597fc443348d1037f834d966a86a7a482e9afc33dbe5191ba10462349bbbea
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.

2.332 × 10⁹⁹(100-digit number)
23326292727347618203…16504642460773653759
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
2.332 × 10⁹⁹(100-digit number)
23326292727347618203…16504642460773653759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.665 × 10⁹⁹(100-digit number)
46652585454695236406…33009284921547307519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
9.330 × 10⁹⁹(100-digit number)
93305170909390472813…66018569843094615039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.866 × 10¹⁰⁰(101-digit number)
18661034181878094562…32037139686189230079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.732 × 10¹⁰⁰(101-digit number)
37322068363756189125…64074279372378460159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
7.464 × 10¹⁰⁰(101-digit number)
74644136727512378250…28148558744756920319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.492 × 10¹⁰¹(102-digit number)
14928827345502475650…56297117489513840639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.985 × 10¹⁰¹(102-digit number)
29857654691004951300…12594234979027681279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.971 × 10¹⁰¹(102-digit number)
59715309382009902600…25188469958055362559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.194 × 10¹⁰²(103-digit number)
11943061876401980520…50376939916110725119
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:57,726,914 XPM·at block #6,810,353 · updates every 60s
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