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Block #2,650,205

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/5/2018, 8:48:32 PM Β· Difficulty 11.7586 Β· 4,191,657 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c53885f4a8804c529bb5a7a20f5b9fb123ca9174648f49cfdfe9a2694f41764e
View on Chainz β†—

Height

#2,650,205

Difficulty

11.758606

Transactions

1

Size

200 B

Version

2

Bits

0bc233fc

Nonce

480,823,400

Timestamp

5/5/2018, 8:48:32 PM

Confirmations

4,191,657

Mined by

⛏️ P2SHALQGpaT6bUeDR1X73XRmMe4Z6w9dLVU1B9

Merkle Root

50be57ad5d45b908862749dbebe0ad1be366f568b4cf185ad4484a806445f75a
Transactions (1)
Coinbase50be57ad5d45b9…484a806445f75a
1 in β†’ 1 out7.2200 XPM109 B
ALQGpaT6…9dLVU1B9
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.

1.060 Γ— 10⁹⁷(98-digit number)
10606094292326337327…91516648503110671359
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
1.060 Γ— 10⁹⁷(98-digit number)
10606094292326337327…91516648503110671359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.121 Γ— 10⁹⁷(98-digit number)
21212188584652674654…83033297006221342719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.242 Γ— 10⁹⁷(98-digit number)
42424377169305349308…66066594012442685439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.484 Γ— 10⁹⁷(98-digit number)
84848754338610698617…32133188024885370879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.696 Γ— 10⁹⁸(99-digit number)
16969750867722139723…64266376049770741759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.393 Γ— 10⁹⁸(99-digit number)
33939501735444279446…28532752099541483519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.787 Γ— 10⁹⁸(99-digit number)
67879003470888558893…57065504199082967039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.357 Γ— 10⁹⁹(100-digit number)
13575800694177711778…14131008398165934079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.715 Γ— 10⁹⁹(100-digit number)
27151601388355423557…28262016796331868159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.430 Γ— 10⁹⁹(100-digit number)
54303202776710847115…56524033592663736319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.086 Γ— 10¹⁰⁰(101-digit number)
10860640555342169423…13048067185327472639
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:57,979,273 XPMΒ·at block #6,841,861 Β· updates every 60s
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