XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,413,498

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/14/2016, 9:25:05 PM Β· Difficulty 10.8021 Β· 5,395,789 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
25989363e0f7d7d1afbfec9909bfd33112feb8969b8ffd8d2b08aefadbfbb770
View on Chainz β†—

Height

#1,413,498

Difficulty

10.802106

Transactions

1

Size

199 B

Version

2

Bits

0acd56d2

Nonce

387,439,776

Timestamp

1/14/2016, 9:25:05 PM

Confirmations

5,395,789

Mined by

⛏️ P2SHAW8VydQwvVSNpwTKzZfM9Dr31JCWRm51qC

Merkle Root

cff6fc4bf4f0e678c9f5e36ca3166e4105be6ae668a5d7e3670fb754cc3647c2
Transactions (1)
Coinbasecff6fc4bf4f0e6…0fb754cc3647c2
1 in β†’ 1 out8.5600 XPM109 B
AW8VydQw…CWRm51qC
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.

3.111 Γ— 10⁹⁴(95-digit number)
31110441637053216229…78503744434799273521
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
3.111 Γ— 10⁹⁴(95-digit number)
31110441637053216229…78503744434799273521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.222 Γ— 10⁹⁴(95-digit number)
62220883274106432458…57007488869598547041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.244 Γ— 10⁹⁡(96-digit number)
12444176654821286491…14014977739197094081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.488 Γ— 10⁹⁡(96-digit number)
24888353309642572983…28029955478394188161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.977 Γ— 10⁹⁡(96-digit number)
49776706619285145966…56059910956788376321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.955 Γ— 10⁹⁡(96-digit number)
99553413238570291933…12119821913576752641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.991 Γ— 10⁹⁢(97-digit number)
19910682647714058386…24239643827153505281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.982 Γ— 10⁹⁢(97-digit number)
39821365295428116773…48479287654307010561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.964 Γ— 10⁹⁢(97-digit number)
79642730590856233547…96958575308614021121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.592 Γ— 10⁹⁷(98-digit number)
15928546118171246709…93917150617228042241
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:57,718,365 XPMΒ·at block #6,809,286 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.
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