Block #1,094,512

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 6/7/2015, 11:23:28 PM · Difficulty 10.7452 · 5,712,391 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ea40d8d7951d7ae4c03199c565eb3d5c9a74f8b28a444c1f8958a62a6ec918e0

Height

#1,094,512

Difficulty

10.745173

Transactions

1

Size

242 B

Version

2

Bits

0abec3b0

Nonce

193,515,329

Timestamp

6/7/2015, 11:23:28 PM

Confirmations

5,712,391

Merkle Root

7281c4e3c5526ccd10f51433df8859f8e90b918e2a04d2104452691a8ce586b9
Transactions (1)
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.

3.180 × 10⁹⁵(96-digit number)
31805906767056833718…80197649972445833279
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
3.180 × 10⁹⁵(96-digit number)
31805906767056833718…80197649972445833279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
6.361 × 10⁹⁵(96-digit number)
63611813534113667437…60395299944891666559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.272 × 10⁹⁶(97-digit number)
12722362706822733487…20790599889783333119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.544 × 10⁹⁶(97-digit number)
25444725413645466974…41581199779566666239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.088 × 10⁹⁶(97-digit number)
50889450827290933949…83162399559133332479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.017 × 10⁹⁷(98-digit number)
10177890165458186789…66324799118266664959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.035 × 10⁹⁷(98-digit number)
20355780330916373579…32649598236533329919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.071 × 10⁹⁷(98-digit number)
40711560661832747159…65299196473066659839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
8.142 × 10⁹⁷(98-digit number)
81423121323665494319…30598392946133319679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.628 × 10⁹⁸(99-digit number)
16284624264733098863…61196785892266639359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
3.256 × 10⁹⁸(99-digit number)
32569248529466197727…22393571784533278719
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 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
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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,699,334 XPM·at block #6,806,902 · updates every 60s
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