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Block #2,526,291

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/18/2018, 2:16:17 AM Β· Difficulty 10.9838 Β· 4,315,103 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f7222af5c60f00b8b83657bddfcb49291a8d099b653146f5630c736fa8dd384a
View on Chainz β†—

Height

#2,526,291

Difficulty

10.983781

Transactions

2

Size

423 B

Version

2

Bits

0afbd90e

Nonce

46,951,586

Timestamp

2/18/2018, 2:16:17 AM

Confirmations

4,315,103

Mined by

⛏️ P2SHAG5PGw755aTKwBF9TD3Qx1C2Xeb6p2QM5r

Merkle Root

46097bcc5ca009b41b191fff0960690e1931b611ab234b391d224482901fe7c4
Transactions (2)
Coinbasea17a846251a014…2975a2f2de3b1e
1 in β†’ 1 out8.2900 XPM109 B
AG5PGw75…b6p2QM5r
14f8bd3c3c79e6…126df8c75340b2
1 in β†’ 2 out1906.7881 XPM225 B
AWUAAaSB…cxywSdnCAKXKra7x…9ww82eaU
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.

5.231 Γ— 10⁹²(93-digit number)
52314382176936786898…77495023388978492919
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
5.231 Γ— 10⁹²(93-digit number)
52314382176936786898…77495023388978492919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.046 Γ— 10⁹³(94-digit number)
10462876435387357379…54990046777956985839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.092 Γ— 10⁹³(94-digit number)
20925752870774714759…09980093555913971679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.185 Γ— 10⁹³(94-digit number)
41851505741549429518…19960187111827943359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.370 Γ— 10⁹³(94-digit number)
83703011483098859037…39920374223655886719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.674 Γ— 10⁹⁴(95-digit number)
16740602296619771807…79840748447311773439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.348 Γ— 10⁹⁴(95-digit number)
33481204593239543614…59681496894623546879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.696 Γ— 10⁹⁴(95-digit number)
66962409186479087229…19362993789247093759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.339 Γ— 10⁹⁡(96-digit number)
13392481837295817445…38725987578494187519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.678 Γ— 10⁹⁡(96-digit number)
26784963674591634891…77451975156988375039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.356 Γ— 10⁹⁡(96-digit number)
53569927349183269783…54903950313976750079
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:57,975,524 XPMΒ·at block #6,841,393 Β· updates every 60s
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