Block #1,273,185

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/8/2015, 11:08:04 PM · Difficulty 10.8228 · 5,552,436 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7934ab00c4c46cbe82068e7001a538f0a354f98b4ae71a67dbc913e29319d524

Height

#1,273,185

Difficulty

10.822827

Transactions

2

Size

778 B

Version

2

Bits

0ad2a4c8

Nonce

1,181,202,448

Timestamp

10/8/2015, 11:08:04 PM

Confirmations

5,552,436

Merkle Root

40c1aa25093f5e1203d43680758f5a6323a759dcf859c58762622ef1f00e244a
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.

3.369 × 10⁹⁴(95-digit number)
33697657033721778198…28011589540590606081
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
3.369 × 10⁹⁴(95-digit number)
33697657033721778198…28011589540590606081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.739 × 10⁹⁴(95-digit number)
67395314067443556397…56023179081181212161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.347 × 10⁹⁵(96-digit number)
13479062813488711279…12046358162362424321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.695 × 10⁹⁵(96-digit number)
26958125626977422559…24092716324724848641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.391 × 10⁹⁵(96-digit number)
53916251253954845118…48185432649449697281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.078 × 10⁹⁶(97-digit number)
10783250250790969023…96370865298899394561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.156 × 10⁹⁶(97-digit number)
21566500501581938047…92741730597798789121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.313 × 10⁹⁶(97-digit number)
43133001003163876094…85483461195597578241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
8.626 × 10⁹⁶(97-digit number)
86266002006327752189…70966922391195156481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.725 × 10⁹⁷(98-digit number)
17253200401265550437…41933844782390312961
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:57,849,070 XPM·at block #6,825,620 · updates every 60s
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