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Block #2,648,674

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/4/2018, 4:33:38 PM Β· Difficulty 11.7662 Β· 4,185,276 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4ed824e5652fa19c55bdfc6ea4c6449f26ed4ee9e44c8d3d0ec018b8483fca7a
View on Chainz β†—

Height

#2,648,674

Difficulty

11.766232

Transactions

1

Size

198 B

Version

2

Bits

0bc427cf

Nonce

94,749,884

Timestamp

5/4/2018, 4:33:38 PM

Confirmations

4,185,276

Mined by

⛏️ P2SHARqFTUygffX9iNi55pB2Avp8iyRVD6wbpW

Merkle Root

23449bb128bbfb6c411673a32c853e113e787045fa96c5703ab5d2d8aa43d2cc
Transactions (1)
Coinbase23449bb128bbfb…b5d2d8aa43d2cc
1 in β†’ 1 out7.2100 XPM109 B
ARqFTUyg…RVD6wbpW
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.

1.192 Γ— 10⁹²(93-digit number)
11925402224942462900…82153068804261412719
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
1.192 Γ— 10⁹²(93-digit number)
11925402224942462900…82153068804261412719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.385 Γ— 10⁹²(93-digit number)
23850804449884925801…64306137608522825439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.770 Γ— 10⁹²(93-digit number)
47701608899769851602…28612275217045650879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.540 Γ— 10⁹²(93-digit number)
95403217799539703204…57224550434091301759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.908 Γ— 10⁹³(94-digit number)
19080643559907940640…14449100868182603519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.816 Γ— 10⁹³(94-digit number)
38161287119815881281…28898201736365207039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.632 Γ— 10⁹³(94-digit number)
76322574239631762563…57796403472730414079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.526 Γ— 10⁹⁴(95-digit number)
15264514847926352512…15592806945460828159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.052 Γ— 10⁹⁴(95-digit number)
30529029695852705025…31185613890921656319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.105 Γ— 10⁹⁴(95-digit number)
61058059391705410050…62371227781843312639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.221 Γ— 10⁹⁡(96-digit number)
12211611878341082010…24742455563686625279
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:57,915,829 XPMΒ·at block #6,833,949 Β· updates every 60s
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