XPM Prime Explorer symbol
XPMPrime Explorer

Block #664,975

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/6/2014, 5:30:49 AM Β· Difficulty 10.9593 Β· 6,151,084 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
42c99617812fdc269b34b023ef91167cf389c3314bc400265bf4255d1bf15291
View on Chainz β†—

Height

#664,975

Difficulty

10.959306

Transactions

2

Size

877 B

Version

2

Bits

0af59515

Nonce

32,189,356

Timestamp

8/6/2014, 5:30:49 AM

Confirmations

6,151,084

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

2f4138e9f8b603f8131fc5932112c793cd8bda84a85c0945a6c438b6406babfe
Transactions (2)
Coinbasee74e4adc69f161…c87d306b4c63dc
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
ab2714297a4cd1…a14dd03006445c
4 in β†’ 2 out553.7415 XPM671 B
AHyjDXQG…n3K3AGTcATQR6iVT…rXs44xxY
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.

3.048 Γ— 10⁹⁴(95-digit number)
30486958172734144349…59962777699258577301
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
3.048 Γ— 10⁹⁴(95-digit number)
30486958172734144349…59962777699258577301
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.097 Γ— 10⁹⁴(95-digit number)
60973916345468288698…19925555398517154601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.219 Γ— 10⁹⁡(96-digit number)
12194783269093657739…39851110797034309201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.438 Γ— 10⁹⁡(96-digit number)
24389566538187315479…79702221594068618401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.877 Γ— 10⁹⁡(96-digit number)
48779133076374630959…59404443188137236801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.755 Γ— 10⁹⁡(96-digit number)
97558266152749261918…18808886376274473601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.951 Γ— 10⁹⁢(97-digit number)
19511653230549852383…37617772752548947201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.902 Γ— 10⁹⁢(97-digit number)
39023306461099704767…75235545505097894401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.804 Γ— 10⁹⁢(97-digit number)
78046612922199409534…50471091010195788801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.560 Γ— 10⁹⁷(98-digit number)
15609322584439881906…00942182020391577601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.121 Γ— 10⁹⁷(98-digit number)
31218645168879763813…01884364040783155201
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:57,772,588 XPMΒ·at block #6,816,058 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy