XPM Prime Explorer symbol
XPMPrime Explorer

Block #200,304

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/8/2013, 10:22:43 PM Β· Difficulty 9.8894 Β· 6,624,453 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f7535371f3f6889f1abd959586899f46d03ffffba22b0ec9cd9647938295aed2
View on Chainz β†—

Height

#200,304

Difficulty

9.889367

Transactions

2

Size

391 B

Version

2

Bits

09e3ad92

Nonce

121,222

Timestamp

10/8/2013, 10:22:43 PM

Confirmations

6,624,453

Mined by

⛏️ P2SHAHNdTz9RdyhMpsaRttP7HwiXvgDHU2jpcA

Merkle Root

354f4f555d5f4b52aa5e92ad30d450ced9b23cf5f846c77805944de75e0293b1
Transactions (2)
Coinbase5f57fc6b6cc1de…feba6f75f0faf5
1 in β†’ 1 out10.2200 XPM109 B
AHNdTz9R…DHU2jpcA
9b7b04e13ec319…71fdfb0c8c00b1
1 in β†’ 1 out25.0061 XPM192 B
ASR2dSpg…y4caQsoo
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.

7.492 Γ— 10⁹³(94-digit number)
74924342424377732296…39356756586138403921
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
7.492 Γ— 10⁹³(94-digit number)
74924342424377732296…39356756586138403921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.498 Γ— 10⁹⁴(95-digit number)
14984868484875546459…78713513172276807841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.996 Γ— 10⁹⁴(95-digit number)
29969736969751092918…57427026344553615681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.993 Γ— 10⁹⁴(95-digit number)
59939473939502185836…14854052689107231361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.198 Γ— 10⁹⁡(96-digit number)
11987894787900437167…29708105378214462721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.397 Γ— 10⁹⁡(96-digit number)
23975789575800874334…59416210756428925441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.795 Γ— 10⁹⁡(96-digit number)
47951579151601748669…18832421512857850881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.590 Γ— 10⁹⁡(96-digit number)
95903158303203497339…37664843025715701761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.918 Γ— 10⁹⁢(97-digit number)
19180631660640699467…75329686051431403521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.836 Γ— 10⁹⁢(97-digit number)
38361263321281398935…50659372102862807041
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:57,842,127 XPMΒ·at block #6,824,756 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