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Block #2,468,647

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/11/2018, 11:25:20 PM Β· Difficulty 10.9601 Β· 4,374,304 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5521037c24954b3c136b5f8bb3d054562b0fd3977aac93bc7003c5c1b77772ca
View on Chainz β†—

Height

#2,468,647

Difficulty

10.960075

Transactions

2

Size

426 B

Version

2

Bits

0af5c772

Nonce

1,602,420,982

Timestamp

1/11/2018, 11:25:20 PM

Confirmations

4,374,304

Mined by

⛏️ P2SHAbWsT6JZGcJyhK5WHCdQbZArJoh7iL6db4

Merkle Root

792604cc0df7f0138ae8b58b7ddd416245508d18474051a1e809242e96e00b4c
Transactions (2)
Coinbase33ecf24aa13d6e…41381dda8d54ff
1 in β†’ 1 out8.3200 XPM109 B
AbWsT6JZ…h7iL6db4
33502c5584dfcf…37b192307efea8
1 in β†’ 2 out5306.7206 XPM226 B
AVqG1GJ7…ya2ZueAvAd1nzX5a…3wgBTFzd
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.

3.010 Γ— 10⁹⁢(97-digit number)
30102588517092826867…40663476282656853761
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
3.010 Γ— 10⁹⁢(97-digit number)
30102588517092826867…40663476282656853761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.020 Γ— 10⁹⁢(97-digit number)
60205177034185653735…81326952565313707521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.204 Γ— 10⁹⁷(98-digit number)
12041035406837130747…62653905130627415041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.408 Γ— 10⁹⁷(98-digit number)
24082070813674261494…25307810261254830081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.816 Γ— 10⁹⁷(98-digit number)
48164141627348522988…50615620522509660161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.632 Γ— 10⁹⁷(98-digit number)
96328283254697045976…01231241045019320321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.926 Γ— 10⁹⁸(99-digit number)
19265656650939409195…02462482090038640641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.853 Γ— 10⁹⁸(99-digit number)
38531313301878818390…04924964180077281281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.706 Γ— 10⁹⁸(99-digit number)
77062626603757636781…09849928360154562561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.541 Γ— 10⁹⁹(100-digit number)
15412525320751527356…19699856720309125121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.082 Γ— 10⁹⁹(100-digit number)
30825050641503054712…39399713440618250241
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:57,987,960 XPMΒ·at block #6,842,950 Β· updates every 60s
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