Block #1,488,226

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/8/2016, 2:20:01 AM · Difficulty 10.7155 · 5,345,239 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
51790740386a278506dbbc28cd838d26a1b81bdac235e26972c132f2a2c0582e

Height

#1,488,226

Difficulty

10.715542

Transactions

2

Size

1.43 KB

Version

2

Bits

0ab72dc4

Nonce

249,983,014

Timestamp

3/8/2016, 2:20:01 AM

Confirmations

5,345,239

Merkle Root

03e3ad9321423cbd30bfcaedfafa6837c90702e77910ef180c87a15b7d866d5e
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.

2.551 × 10⁹⁴(95-digit number)
25519213929307418249…03775302790347609521
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
2.551 × 10⁹⁴(95-digit number)
25519213929307418249…03775302790347609521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.103 × 10⁹⁴(95-digit number)
51038427858614836498…07550605580695219041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.020 × 10⁹⁵(96-digit number)
10207685571722967299…15101211161390438081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.041 × 10⁹⁵(96-digit number)
20415371143445934599…30202422322780876161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.083 × 10⁹⁵(96-digit number)
40830742286891869198…60404844645561752321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
8.166 × 10⁹⁵(96-digit number)
81661484573783738397…20809689291123504641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.633 × 10⁹⁶(97-digit number)
16332296914756747679…41619378582247009281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.266 × 10⁹⁶(97-digit number)
32664593829513495358…83238757164494018561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.532 × 10⁹⁶(97-digit number)
65329187659026990717…66477514328988037121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.306 × 10⁹⁷(98-digit number)
13065837531805398143…32955028657976074241
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 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
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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,911,921 XPM·at block #6,833,464 · updates every 60s
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