Block #377,840

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/27/2014, 10:16:30 AM · Difficulty 10.4183 · 6,428,374 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a84629d2695eb572d5ec58e0ce65901b1651b643a8883b08549e3ca15d00ff69

Height

#377,840

Difficulty

10.418281

Transactions

3

Size

769 B

Version

2

Bits

0a6b1471

Nonce

18,497

Timestamp

1/27/2014, 10:16:30 AM

Confirmations

6,428,374

Merkle Root

5993995eb33c60bdda3c3c47df5f0aaa5d5a88f5b6921f1d2afd5e300d404d80
Transactions (3)
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.

9.531 × 10⁹⁵(96-digit number)
95318927404448847996…14756617842865177781
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
9.531 × 10⁹⁵(96-digit number)
95318927404448847996…14756617842865177781
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.906 × 10⁹⁶(97-digit number)
19063785480889769599…29513235685730355561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.812 × 10⁹⁶(97-digit number)
38127570961779539198…59026471371460711121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.625 × 10⁹⁶(97-digit number)
76255141923559078396…18052942742921422241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.525 × 10⁹⁷(98-digit number)
15251028384711815679…36105885485842844481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.050 × 10⁹⁷(98-digit number)
30502056769423631358…72211770971685688961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.100 × 10⁹⁷(98-digit number)
61004113538847262717…44423541943371377921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.220 × 10⁹⁸(99-digit number)
12200822707769452543…88847083886742755841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.440 × 10⁹⁸(99-digit number)
24401645415538905087…77694167773485511681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.880 × 10⁹⁸(99-digit number)
48803290831077810174…55388335546971023361
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:57,693,792 XPM·at block #6,806,213 · updates every 60s
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