Block #2,110,009

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 5/10/2017, 12:22:59 PM · Difficulty 10.9018 · 4,726,974 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1529ca143a20dc9ce3a02a1f1dc7eb8cbab5172e645dba33791e5e70903b841c

Height

#2,110,009

Difficulty

10.901815

Transactions

2

Size

424 B

Version

2

Bits

0ae6dd61

Nonce

1,726,237,202

Timestamp

5/10/2017, 12:22:59 PM

Confirmations

4,726,974

Merkle Root

c681c7a0fdbfb85e2d8c8578325543432bcff96c482b0d881b374dd43f49e99e
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.

1.210 × 10⁹⁵(96-digit number)
12100768873464567842…29418809536005345599
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
1.210 × 10⁹⁵(96-digit number)
12100768873464567842…29418809536005345599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.420 × 10⁹⁵(96-digit number)
24201537746929135684…58837619072010691199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.840 × 10⁹⁵(96-digit number)
48403075493858271368…17675238144021382399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
9.680 × 10⁹⁵(96-digit number)
96806150987716542737…35350476288042764799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.936 × 10⁹⁶(97-digit number)
19361230197543308547…70700952576085529599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.872 × 10⁹⁶(97-digit number)
38722460395086617094…41401905152171059199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
7.744 × 10⁹⁶(97-digit number)
77444920790173234189…82803810304342118399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.548 × 10⁹⁷(98-digit number)
15488984158034646837…65607620608684236799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.097 × 10⁹⁷(98-digit number)
30977968316069293675…31215241217368473599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
6.195 × 10⁹⁷(98-digit number)
61955936632138587351…62430482434736947199
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:57,940,164 XPM·at block #6,836,982 · updates every 60s
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