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Block #2,725,622

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/28/2018, 7:48:26 PM Β· Difficulty 11.6233 Β· 4,107,591 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
44601864b98135851623cfe589b756818c04711b84efc5a610e485c199e59f07
View on Chainz β†—

Height

#2,725,622

Difficulty

11.623348

Transactions

2

Size

719 B

Version

2

Bits

0b9f93c0

Nonce

112,937,161

Timestamp

6/28/2018, 7:48:26 PM

Confirmations

4,107,591

Mined by

⛏️ P2SHAeT2xoP4wbgcSJoBJ3D4D1B7hjC336MZcp

Merkle Root

8a72991f2b42e28bf95d4d83c8b5b1d1e1bed274bf4194253e9fadccc136e78a
Transactions (2)
Coinbase6e08cc4228e3c3…57051ab1b31098
1 in β†’ 1 out7.4000 XPM109 B
AeT2xoP4…C336MZcp
0302bb6a040820…10c297f8fcd0af
3 in β†’ 2 out451.0099 XPM520 B
AUxvVom2…QCmyJGZWAMacMFhM…iFNVuut4
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.

2.147 Γ— 10⁹⁡(96-digit number)
21475522649186986606…21229154732467937279
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
2.147 Γ— 10⁹⁡(96-digit number)
21475522649186986606…21229154732467937279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.295 Γ— 10⁹⁡(96-digit number)
42951045298373973212…42458309464935874559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.590 Γ— 10⁹⁡(96-digit number)
85902090596747946425…84916618929871749119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.718 Γ— 10⁹⁢(97-digit number)
17180418119349589285…69833237859743498239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.436 Γ— 10⁹⁢(97-digit number)
34360836238699178570…39666475719486996479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.872 Γ— 10⁹⁢(97-digit number)
68721672477398357140…79332951438973992959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.374 Γ— 10⁹⁷(98-digit number)
13744334495479671428…58665902877947985919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.748 Γ— 10⁹⁷(98-digit number)
27488668990959342856…17331805755895971839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.497 Γ— 10⁹⁷(98-digit number)
54977337981918685712…34663611511791943679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.099 Γ— 10⁹⁸(99-digit number)
10995467596383737142…69327223023583887359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.199 Γ— 10⁹⁸(99-digit number)
21990935192767474284…38654446047167774719
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,909,890 XPMΒ·at block #6,833,212 Β· updates every 60s
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