Block #2,460,271

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 1/6/2018, 2:18:45 PM · Difficulty 10.9545 · 4,381,645 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e5272a2684451d5d0316366c32390eb18a264d35cfd07462479262b2dd00c8da

Height

#2,460,271

Difficulty

10.954488

Transactions

2

Size

390 B

Version

2

Bits

0af45959

Nonce

928,115,963

Timestamp

1/6/2018, 2:18:45 PM

Confirmations

4,381,645

Merkle Root

05ee02e274654c1b233999bd2281395eb1041ae0f68d54b71c9f8342bd30e7f2
Transactions (2)
1 in → 1 out8.3300 XPM110 B
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.

2.007 × 10⁹³(94-digit number)
20077632361078941388…17011071179730163441
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
2.007 × 10⁹³(94-digit number)
20077632361078941388…17011071179730163441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.015 × 10⁹³(94-digit number)
40155264722157882777…34022142359460326881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
8.031 × 10⁹³(94-digit number)
80310529444315765555…68044284718920653761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.606 × 10⁹⁴(95-digit number)
16062105888863153111…36088569437841307521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.212 × 10⁹⁴(95-digit number)
32124211777726306222…72177138875682615041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.424 × 10⁹⁴(95-digit number)
64248423555452612444…44354277751365230081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.284 × 10⁹⁵(96-digit number)
12849684711090522488…88708555502730460161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.569 × 10⁹⁵(96-digit number)
25699369422181044977…77417111005460920321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.139 × 10⁹⁵(96-digit number)
51398738844362089955…54834222010921840641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.027 × 10⁹⁶(97-digit number)
10279747768872417991…09668444021843681281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
2.055 × 10⁹⁶(97-digit number)
20559495537744835982…19336888043687362561
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:57,979,703 XPM·at block #6,841,915 · updates every 60s
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