Block #1,231,445

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 9/11/2015, 7:42:26 AM · Difficulty 10.7383 · 5,576,584 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c83c9d233d19feb704869744851142b2b28ee4243c20f42b1be022729e998b14

Height

#1,231,445

Difficulty

10.738254

Transactions

2

Size

581 B

Version

2

Bits

0abcfe37

Nonce

145,138,418

Timestamp

9/11/2015, 7:42:26 AM

Confirmations

5,576,584

Merkle Root

e498e77e5e90bbe86dc65c07ef1e557125b1996313c4908f73d3ad4963baea7b
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.

9.578 × 10⁹⁷(98-digit number)
95784579102993224680…33147713541965900799
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
9.578 × 10⁹⁷(98-digit number)
95784579102993224680…33147713541965900799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.915 × 10⁹⁸(99-digit number)
19156915820598644936…66295427083931801599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.831 × 10⁹⁸(99-digit number)
38313831641197289872…32590854167863603199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.662 × 10⁹⁸(99-digit number)
76627663282394579744…65181708335727206399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.532 × 10⁹⁹(100-digit number)
15325532656478915948…30363416671454412799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.065 × 10⁹⁹(100-digit number)
30651065312957831897…60726833342908825599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
6.130 × 10⁹⁹(100-digit number)
61302130625915663795…21453666685817651199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.226 × 10¹⁰⁰(101-digit number)
12260426125183132759…42907333371635302399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.452 × 10¹⁰⁰(101-digit number)
24520852250366265518…85814666743270604799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.904 × 10¹⁰⁰(101-digit number)
49041704500732531036…71629333486541209599
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:57,708,276 XPM·at block #6,808,028 · updates every 60s
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