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Block #2,574,602

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/19/2018, 7:49:04 PM Β· Difficulty 10.9953 Β· 4,268,650 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8a8887a22a08a7b9c16206b9d78fca326ac5db8453cf49ab5a825664b9cde8ca
View on Chainz β†—

Height

#2,574,602

Difficulty

10.995337

Transactions

1

Size

201 B

Version

2

Bits

0afece68

Nonce

676,498,824

Timestamp

3/19/2018, 7:49:04 PM

Confirmations

4,268,650

Mined by

⛏️ P2SHARwYiCkcFzbZUevpfLcxjeSXZv6taWdLSM

Merkle Root

cdd6e4d3d4daa5fee9d9506f51fceac63781cba5f6a856a74462c8b1a4d65bb5
Transactions (1)
Coinbasecdd6e4d3d4daa5…62c8b1a4d65bb5
1 in β†’ 1 out8.2600 XPM110 B
ARwYiCkc…6taWdLSM
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.

1.699 Γ— 10⁹⁷(98-digit number)
16994486433663840359…88452849514782458879
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
1.699 Γ— 10⁹⁷(98-digit number)
16994486433663840359…88452849514782458879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.398 Γ— 10⁹⁷(98-digit number)
33988972867327680719…76905699029564917759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.797 Γ— 10⁹⁷(98-digit number)
67977945734655361438…53811398059129835519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.359 Γ— 10⁹⁸(99-digit number)
13595589146931072287…07622796118259671039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.719 Γ— 10⁹⁸(99-digit number)
27191178293862144575…15245592236519342079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.438 Γ— 10⁹⁸(99-digit number)
54382356587724289150…30491184473038684159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.087 Γ— 10⁹⁹(100-digit number)
10876471317544857830…60982368946077368319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.175 Γ— 10⁹⁹(100-digit number)
21752942635089715660…21964737892154736639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.350 Γ— 10⁹⁹(100-digit number)
43505885270179431320…43929475784309473279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.701 Γ— 10⁹⁹(100-digit number)
87011770540358862641…87858951568618946559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.740 Γ— 10¹⁰⁰(101-digit number)
17402354108071772528…75717903137237893119
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:57,990,393 XPMΒ·at block #6,843,251 Β· updates every 60s
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