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Block #2,479,157

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/18/2018, 6:12:12 PM Β· Difficulty 10.9658 Β· 4,361,415 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
69cab1190b00ba8d81620f5e6214c4e13d3e43146fc8a16d3f9afb2aa95a8931
View on Chainz β†—

Height

#2,479,157

Difficulty

10.965848

Transactions

2

Size

573 B

Version

2

Bits

0af741cb

Nonce

615,031,718

Timestamp

1/18/2018, 6:12:12 PM

Confirmations

4,361,415

Mined by

⛏️ P2SHAQyut1XgigB3MU99Wfi3owDdLUjqg4hbrH

Merkle Root

0f646b355bd9d7fc1bdaee3de907671585e275c162d717a5ae762a2b35101057
Transactions (2)
Coinbase82308c63471dc3…46cd2f7e101055
1 in β†’ 1 out8.3100 XPM110 B
AQyut1Xg…jqg4hbrH
468f48eb5a080c…08fde7ce28e060
2 in β†’ 2 out37.6199 XPM373 B
APXQzS1Y…EUuSwnpiAVAY4W5s…7sSNwctv
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.

1.912 Γ— 10⁹⁴(95-digit number)
19128350028781503137…59973916877952263401
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
1.912 Γ— 10⁹⁴(95-digit number)
19128350028781503137…59973916877952263401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.825 Γ— 10⁹⁴(95-digit number)
38256700057563006275…19947833755904526801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.651 Γ— 10⁹⁴(95-digit number)
76513400115126012551…39895667511809053601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.530 Γ— 10⁹⁡(96-digit number)
15302680023025202510…79791335023618107201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.060 Γ— 10⁹⁡(96-digit number)
30605360046050405020…59582670047236214401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.121 Γ— 10⁹⁡(96-digit number)
61210720092100810040…19165340094472428801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.224 Γ— 10⁹⁢(97-digit number)
12242144018420162008…38330680188944857601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.448 Γ— 10⁹⁢(97-digit number)
24484288036840324016…76661360377889715201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.896 Γ— 10⁹⁢(97-digit number)
48968576073680648032…53322720755779430401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.793 Γ— 10⁹⁢(97-digit number)
97937152147361296065…06645441511558860801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.958 Γ— 10⁹⁷(98-digit number)
19587430429472259213…13290883023117721601
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:57,968,911 XPMΒ·at block #6,840,571 Β· updates every 60s
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