Block #939,126

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/16/2015, 4:03:11 PM · Difficulty 10.9006 · 5,866,051 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3724e3236933cff19811bcdaf487f413ad76f336a694295761a20b9570ed0569

Height

#939,126

Difficulty

10.900633

Transactions

4

Size

850 B

Version

2

Bits

0ae68fe6

Nonce

101,624,755

Timestamp

2/16/2015, 4:03:11 PM

Confirmations

5,866,051

Merkle Root

0d1ca2f2bfcb0c57627fff0d8324d40c07b73cb4bf1e82d55b6c8306e8675391
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.

1.650 × 10⁹⁷(98-digit number)
16501156794849696214…94044233482288660479
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
1.650 × 10⁹⁷(98-digit number)
16501156794849696214…94044233482288660479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.300 × 10⁹⁷(98-digit number)
33002313589699392428…88088466964577320959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
6.600 × 10⁹⁷(98-digit number)
66004627179398784856…76176933929154641919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.320 × 10⁹⁸(99-digit number)
13200925435879756971…52353867858309283839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.640 × 10⁹⁸(99-digit number)
26401850871759513942…04707735716618567679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
5.280 × 10⁹⁸(99-digit number)
52803701743519027885…09415471433237135359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.056 × 10⁹⁹(100-digit number)
10560740348703805577…18830942866474270719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.112 × 10⁹⁹(100-digit number)
21121480697407611154…37661885732948541439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.224 × 10⁹⁹(100-digit number)
42242961394815222308…75323771465897082879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
8.448 × 10⁹⁹(100-digit number)
84485922789630444616…50647542931794165759
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:57,685,485 XPM·at block #6,805,176 · updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.