Block #467,837

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/31/2014, 2:24:24 AM · Difficulty 10.4314 · 6,328,749 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
87ebd7de1756e59a57e42777e9fb891f90835d65e4ed52a9cf26ea066687c587

Height

#467,837

Difficulty

10.431382

Transactions

1

Size

970 B

Version

2

Bits

0a6e6f14

Nonce

62,900

Timestamp

3/31/2014, 2:24:24 AM

Confirmations

6,328,749

Merkle Root

b038b8ebe3888635a6088e8f79b79158481abebfc5748a8f1894b742a85f7f81
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.

6.082 × 10⁹⁶(97-digit number)
60821842828079367670…21825466291820671999
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
6.082 × 10⁹⁶(97-digit number)
60821842828079367670…21825466291820671999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.216 × 10⁹⁷(98-digit number)
12164368565615873534…43650932583641343999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.432 × 10⁹⁷(98-digit number)
24328737131231747068…87301865167282687999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.865 × 10⁹⁷(98-digit number)
48657474262463494136…74603730334565375999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
9.731 × 10⁹⁷(98-digit number)
97314948524926988273…49207460669130751999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.946 × 10⁹⁸(99-digit number)
19462989704985397654…98414921338261503999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.892 × 10⁹⁸(99-digit number)
38925979409970795309…96829842676523007999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
7.785 × 10⁹⁸(99-digit number)
77851958819941590618…93659685353046015999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.557 × 10⁹⁹(100-digit number)
15570391763988318123…87319370706092031999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.114 × 10⁹⁹(100-digit number)
31140783527976636247…74638741412184063999
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:57,616,691 XPM·at block #6,796,585 · updates every 60s
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