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Block #1,150,838

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/11/2015, 6:08:22 PM Β· Difficulty 10.9456 Β· 5,665,965 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5cb50020100572813d01a5ba07335c705e226771b74834df1a85eb895e1f14b6
View on Chainz β†—

Height

#1,150,838

Difficulty

10.945619

Transactions

2

Size

689 B

Version

2

Bits

0af21418

Nonce

350,121,996

Timestamp

7/11/2015, 6:08:22 PM

Confirmations

5,665,965

Mined by

⛏️ P2SHAZbaCC9YRRy1LavV4JQYhpzSR5m6kRxm85

Merkle Root

f37a4beb6a7ed457eace6e1e0c69b367b64b69d4b62231474cb91d2caff62f41
Transactions (2)
Coinbase9f3eab36c48e57…6da6d91627e4e9
1 in β†’ 1 out8.3400 XPM110 B
AZbaCC9Y…m6kRxm85
d01baaacf1dfd0…e5f360b16f4c8b
3 in β†’ 1 out180.1864 XPM489 B
AX7mEs41…FWw8mZZH
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.506 Γ— 10⁹⁴(95-digit number)
15068154943590901230…50394369787501552641
Discovered Prime Numbers
p_k = 2^k Γ— 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
1.506 Γ— 10⁹⁴(95-digit number)
15068154943590901230…50394369787501552641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.013 Γ— 10⁹⁴(95-digit number)
30136309887181802460…00788739575003105281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.027 Γ— 10⁹⁴(95-digit number)
60272619774363604921…01577479150006210561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.205 Γ— 10⁹⁡(96-digit number)
12054523954872720984…03154958300012421121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.410 Γ— 10⁹⁡(96-digit number)
24109047909745441968…06309916600024842241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.821 Γ— 10⁹⁡(96-digit number)
48218095819490883937…12619833200049684481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.643 Γ— 10⁹⁡(96-digit number)
96436191638981767874…25239666400099368961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.928 Γ— 10⁹⁢(97-digit number)
19287238327796353574…50479332800198737921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.857 Γ— 10⁹⁢(97-digit number)
38574476655592707149…00958665600397475841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.714 Γ— 10⁹⁢(97-digit number)
77148953311185414299…01917331200794951681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.542 Γ— 10⁹⁷(98-digit number)
15429790662237082859…03834662401589903361
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,778,460 XPMΒ·at block #6,816,802 Β· updates every 60s
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