Block #1,576,060

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 5/8/2016, 10:41:05 AM · Difficulty 10.6890 · 5,267,565 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b288561d16ac8bf8dabeb36888761a93b014395988be031cc16f2e635f0608d8

Height

#1,576,060

Difficulty

10.689038

Transactions

2

Size

1.18 KB

Version

2

Bits

0ab064ce

Nonce

424,159,466

Timestamp

5/8/2016, 10:41:05 AM

Confirmations

5,267,565

Merkle Root

a9288f1b3c73f1872515091a0a99efc4a816e18d59bd494b8f192997c1b3cbbd
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.

4.962 × 10⁹⁵(96-digit number)
49626956105636688006…53318762286478575359
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
4.962 × 10⁹⁵(96-digit number)
49626956105636688006…53318762286478575359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
9.925 × 10⁹⁵(96-digit number)
99253912211273376012…06637524572957150719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.985 × 10⁹⁶(97-digit number)
19850782442254675202…13275049145914301439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.970 × 10⁹⁶(97-digit number)
39701564884509350405…26550098291828602879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
7.940 × 10⁹⁶(97-digit number)
79403129769018700810…53100196583657205759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.588 × 10⁹⁷(98-digit number)
15880625953803740162…06200393167314411519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.176 × 10⁹⁷(98-digit number)
31761251907607480324…12400786334628823039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
6.352 × 10⁹⁷(98-digit number)
63522503815214960648…24801572669257646079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.270 × 10⁹⁸(99-digit number)
12704500763042992129…49603145338515292159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.540 × 10⁹⁸(99-digit number)
25409001526085984259…99206290677030584319
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 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
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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,993,366 XPM·at block #6,843,624 · updates every 60s
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