Block #2,486,102

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 1/23/2018, 9:08:32 AM · Difficulty 10.9679 · 4,355,320 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
73b723b6ef38eb202b91232e83f404551f264d051cc43d0b25c854ad6570c842

Height

#2,486,102

Difficulty

10.967946

Transactions

4

Size

776 B

Version

2

Bits

0af7cb53

Nonce

375,192,385

Timestamp

1/23/2018, 9:08:32 AM

Confirmations

4,355,320

Merkle Root

f9d78d74b2e01719f901f94a0627099dc631bf06bb7a017d2058d6fda0cb2f08
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.

7.100 × 10⁹⁶(97-digit number)
71006894614381559032…38216533124986654721
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
7.100 × 10⁹⁶(97-digit number)
71006894614381559032…38216533124986654721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.420 × 10⁹⁷(98-digit number)
14201378922876311806…76433066249973309441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.840 × 10⁹⁷(98-digit number)
28402757845752623612…52866132499946618881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.680 × 10⁹⁷(98-digit number)
56805515691505247225…05732264999893237761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.136 × 10⁹⁸(99-digit number)
11361103138301049445…11464529999786475521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.272 × 10⁹⁸(99-digit number)
22722206276602098890…22929059999572951041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.544 × 10⁹⁸(99-digit number)
45444412553204197780…45858119999145902081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
9.088 × 10⁹⁸(99-digit number)
90888825106408395561…91716239998291804161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.817 × 10⁹⁹(100-digit number)
18177765021281679112…83432479996583608321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.635 × 10⁹⁹(100-digit number)
36355530042563358224…66864959993167216641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
7.271 × 10⁹⁹(100-digit number)
72711060085126716449…33729919986334433281
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the Second 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,975,752 XPM·at block #6,841,421 · updates every 60s
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