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Block #845,021

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/8/2014, 1:59:30 PM Β· Difficulty 10.9726 Β· 5,979,726 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d28e44cf233840ea614629b30e5ad9bcc5e70c77905720d672ae597a7603d5bf
View on Chainz β†—

Height

#845,021

Difficulty

10.972600

Transactions

2

Size

432 B

Version

2

Bits

0af8fc4c

Nonce

2,118,179,029

Timestamp

12/8/2014, 1:59:30 PM

Confirmations

5,979,726

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

88d90000f7c725fa1ffcfa859874b76effbf01e1c19857c2a40b9a372c75e2c8
Transactions (2)
Coinbasef614fb585f0bc4…d289f549999e0f
1 in β†’ 1 out8.3050 XPM116 B
ANSXnLY2…Sd25TjkD
2b78771636c068…9f0776fd4936c3
1 in β†’ 2 out0.1201 XPM225 B
AduDH9up…6NRxnmqYAPWYsrVP…W4Ah3YKa
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.

4.443 Γ— 10⁹⁢(97-digit number)
44433160143833765838…38826667969303649281
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
4.443 Γ— 10⁹⁢(97-digit number)
44433160143833765838…38826667969303649281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.886 Γ— 10⁹⁢(97-digit number)
88866320287667531676…77653335938607298561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.777 Γ— 10⁹⁷(98-digit number)
17773264057533506335…55306671877214597121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.554 Γ— 10⁹⁷(98-digit number)
35546528115067012670…10613343754429194241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.109 Γ— 10⁹⁷(98-digit number)
71093056230134025341…21226687508858388481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.421 Γ— 10⁹⁸(99-digit number)
14218611246026805068…42453375017716776961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.843 Γ— 10⁹⁸(99-digit number)
28437222492053610136…84906750035433553921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.687 Γ— 10⁹⁸(99-digit number)
56874444984107220273…69813500070867107841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.137 Γ— 10⁹⁹(100-digit number)
11374888996821444054…39627000141734215681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.274 Γ— 10⁹⁹(100-digit number)
22749777993642888109…79254000283468431361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.549 Γ— 10⁹⁹(100-digit number)
45499555987285776218…58508000566936862721
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:57,842,047 XPMΒ·at block #6,824,746 Β· updates every 60s
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