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Block #544,029

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/14/2014, 4:46:08 PM Β· Difficulty 10.9493 Β· 6,282,965 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
99fa5e57b6627f012846fa3a97b3527e0ca7e367e59ff262fa00cc759152361c
View on Chainz β†—

Height

#544,029

Difficulty

10.949319

Transactions

1

Size

208 B

Version

2

Bits

0af3068e

Nonce

43,487,654

Timestamp

5/14/2014, 4:46:08 PM

Confirmations

6,282,965

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

a7ddb7511081bc235529870925f98bad2b8a11187077aec072901d899854ec5c
Transactions (1)
Coinbasea7ddb7511081bc…901d899854ec5c
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
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.

4.879 Γ— 10⁹⁸(99-digit number)
48795991866915825723…39424223558000891841
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
4.879 Γ— 10⁹⁸(99-digit number)
48795991866915825723…39424223558000891841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.759 Γ— 10⁹⁸(99-digit number)
97591983733831651446…78848447116001783681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.951 Γ— 10⁹⁹(100-digit number)
19518396746766330289…57696894232003567361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.903 Γ— 10⁹⁹(100-digit number)
39036793493532660578…15393788464007134721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.807 Γ— 10⁹⁹(100-digit number)
78073586987065321157…30787576928014269441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.561 Γ— 10¹⁰⁰(101-digit number)
15614717397413064231…61575153856028538881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.122 Γ— 10¹⁰⁰(101-digit number)
31229434794826128462…23150307712057077761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.245 Γ— 10¹⁰⁰(101-digit number)
62458869589652256925…46300615424114155521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.249 Γ— 10¹⁰¹(102-digit number)
12491773917930451385…92601230848228311041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.498 Γ— 10¹⁰¹(102-digit number)
24983547835860902770…85202461696456622081
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,860,127 XPMΒ·at block #6,826,993 Β· updates every 60s
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