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Block #2,580,270

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/23/2018, 3:08:19 AM Β· Difficulty 11.0364 Β· 4,258,483 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f253593860749f2277c891172ea6c018438a7a053cf5ea69a0024a475ce3d208
View on Chainz β†—

Height

#2,580,270

Difficulty

11.036355

Transactions

1

Size

201 B

Version

2

Bits

0b094e93

Nonce

497,707,398

Timestamp

3/23/2018, 3:08:19 AM

Confirmations

4,258,483

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

3ec3aa28dcfdd1775a851cb7c496bb362836f5ce63b771b24fd6abc43c106fb9
Transactions (1)
Coinbase3ec3aa28dcfdd1…d6abc43c106fb9
1 in β†’ 1 out8.2000 XPM110 B
Adqah8zh…1WwoHJ9t
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.

1.125 Γ— 10⁹⁢(97-digit number)
11254754050143868199…02408997101518906881
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
1.125 Γ— 10⁹⁢(97-digit number)
11254754050143868199…02408997101518906881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.250 Γ— 10⁹⁢(97-digit number)
22509508100287736399…04817994203037813761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.501 Γ— 10⁹⁢(97-digit number)
45019016200575472798…09635988406075627521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.003 Γ— 10⁹⁢(97-digit number)
90038032401150945597…19271976812151255041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.800 Γ— 10⁹⁷(98-digit number)
18007606480230189119…38543953624302510081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.601 Γ— 10⁹⁷(98-digit number)
36015212960460378239…77087907248605020161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.203 Γ— 10⁹⁷(98-digit number)
72030425920920756478…54175814497210040321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.440 Γ— 10⁹⁸(99-digit number)
14406085184184151295…08351628994420080641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.881 Γ— 10⁹⁸(99-digit number)
28812170368368302591…16703257988840161281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.762 Γ— 10⁹⁸(99-digit number)
57624340736736605182…33406515977680322561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.152 Γ— 10⁹⁹(100-digit number)
11524868147347321036…66813031955360645121
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:57,954,282 XPMΒ·at block #6,838,752 Β· updates every 60s
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