Block #901,295

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 1/19/2015, 11:10:32 AM · Difficulty 10.9417 · 5,902,236 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
02b04f083452ebed47e3c6764292de88227d0aa57c1c0571cd19b627c6e481ad

Height

#901,295

Difficulty

10.941717

Transactions

2

Size

1.18 KB

Version

2

Bits

0af11460

Nonce

2,402,306,385

Timestamp

1/19/2015, 11:10:32 AM

Confirmations

5,902,236

Merkle Root

d02920d97824680579bcd97bf771fa3242a9a9d61035e46011e6fd88108631d1
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.

5.965 × 10⁹⁵(96-digit number)
59657502913292901409…79322446888344482879
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
5.965 × 10⁹⁵(96-digit number)
59657502913292901409…79322446888344482879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.193 × 10⁹⁶(97-digit number)
11931500582658580281…58644893776688965759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.386 × 10⁹⁶(97-digit number)
23863001165317160563…17289787553377931519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.772 × 10⁹⁶(97-digit number)
47726002330634321127…34579575106755863039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
9.545 × 10⁹⁶(97-digit number)
95452004661268642254…69159150213511726079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.909 × 10⁹⁷(98-digit number)
19090400932253728450…38318300427023452159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.818 × 10⁹⁷(98-digit number)
38180801864507456901…76636600854046904319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
7.636 × 10⁹⁷(98-digit number)
76361603729014913803…53273201708093808639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.527 × 10⁹⁸(99-digit number)
15272320745802982760…06546403416187617279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.054 × 10⁹⁸(99-digit number)
30544641491605965521…13092806832375234559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
6.108 × 10⁹⁸(99-digit number)
61089282983211931042…26185613664750469119
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:57,672,276 XPM·at block #6,803,530 · updates every 60s
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