XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,784,837

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/8/2018, 12:20:41 PM Β· Difficulty 11.6690 Β· 4,041,274 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2fb7bc0ca48938b070acbe9ab27a50e5848a6998889adcd6036f2756e17d2810
View on Chainz β†—

Height

#2,784,837

Difficulty

11.668995

Transactions

2

Size

906 B

Version

2

Bits

0bab433d

Nonce

1,062,362,383

Timestamp

8/8/2018, 12:20:41 PM

Confirmations

4,041,274

Mined by

⛏️ P2SHAcpDmh7kXCfySZ6SkM2SFowRbw3h7g9bDk

Merkle Root

ea317ac3fcad0e3ea9f44c1eddd47bd273aabb03b9fb7898d43920cc61c0f378
Transactions (2)
Coinbase7e01dfdcd43816…04c3a6382de71e
1 in β†’ 1 out7.3500 XPM110 B
AcpDmh7k…3h7g9bDk
c538ffd96f842a…8a7bb353fb51ed
4 in β†’ 3 out7.3159 XPM705 B
AemQk5YF…RTkGMxRZAPi8C85f…Lg5MDieiASk9H3sY…qUG8r1d4
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.

2.873 Γ— 10⁹⁷(98-digit number)
28734333025182880424…14003649920164106241
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
2.873 Γ— 10⁹⁷(98-digit number)
28734333025182880424…14003649920164106241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.746 Γ— 10⁹⁷(98-digit number)
57468666050365760848…28007299840328212481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.149 Γ— 10⁹⁸(99-digit number)
11493733210073152169…56014599680656424961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.298 Γ— 10⁹⁸(99-digit number)
22987466420146304339…12029199361312849921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.597 Γ— 10⁹⁸(99-digit number)
45974932840292608679…24058398722625699841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.194 Γ— 10⁹⁸(99-digit number)
91949865680585217358…48116797445251399681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.838 Γ— 10⁹⁹(100-digit number)
18389973136117043471…96233594890502799361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.677 Γ— 10⁹⁹(100-digit number)
36779946272234086943…92467189781005598721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.355 Γ— 10⁹⁹(100-digit number)
73559892544468173886…84934379562011197441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.471 Γ— 10¹⁰⁰(101-digit number)
14711978508893634777…69868759124022394881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.942 Γ— 10¹⁰⁰(101-digit number)
29423957017787269554…39737518248044789761
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:57,853,012 XPMΒ·at block #6,826,110 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