XPM Prime Explorer symbol
XPMPrime Explorer

Block #100,671

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/6/2013, 6:51:28 AM Β· Difficulty 9.4346 Β· 6,714,372 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
894512c4fe3711380dc3f256818247f5825bda0f074f74f31d4fef4bb738d9b6
View on Chainz β†—

Height

#100,671

Difficulty

9.434616

Transactions

1

Size

200 B

Version

2

Bits

096f4300

Nonce

198,078

Timestamp

8/6/2013, 6:51:28 AM

Confirmations

6,714,372

Mined by

⛏️ P2SHAXvMMum1Pa5kWMWJFC5uKC4CTEy1ajpFRb

Merkle Root

a9ccba1e71c2e853226231f644f14c18dfd5fea89ff13d8bc69ba70332f28d2f
Transactions (1)
Coinbasea9ccba1e71c2e8…9ba70332f28d2f
1 in β†’ 1 out11.2200 XPM109 B
AXvMMum1…y1ajpFRb
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.

1.080 Γ— 10⁹⁸(99-digit number)
10800133024101935891…85544293636807743981
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
1.080 Γ— 10⁹⁸(99-digit number)
10800133024101935891…85544293636807743981
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.160 Γ— 10⁹⁸(99-digit number)
21600266048203871782…71088587273615487961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.320 Γ— 10⁹⁸(99-digit number)
43200532096407743565…42177174547230975921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.640 Γ— 10⁹⁸(99-digit number)
86401064192815487131…84354349094461951841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.728 Γ— 10⁹⁹(100-digit number)
17280212838563097426…68708698188923903681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.456 Γ— 10⁹⁹(100-digit number)
34560425677126194852…37417396377847807361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.912 Γ— 10⁹⁹(100-digit number)
69120851354252389704…74834792755695614721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.382 Γ— 10¹⁰⁰(101-digit number)
13824170270850477940…49669585511391229441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.764 Γ— 10¹⁰⁰(101-digit number)
27648340541700955881…99339171022782458881
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,764,433 XPMΒ·at block #6,815,042 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