XPM Prime Explorer symbol
XPMPrime Explorer

Block #193,782

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/4/2013, 5:41:04 PM Β· Difficulty 9.8774 Β· 6,607,594 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
825d3205cb609f15fc3c5c0151e5ea2b48e634c2bb89dcbf238f289c2decc486
View on Chainz β†—

Height

#193,782

Difficulty

9.877376

Transactions

2

Size

424 B

Version

2

Bits

09e09baf

Nonce

117,578

Timestamp

10/4/2013, 5:41:04 PM

Confirmations

6,607,594

Mined by

⛏️ P2SHAUm1UXE6PTt11eQB2DXhcmZJbwSTx2UrXW

Merkle Root

e3578df8f27aa36bbbb2a8db1f644920088e190853611796e643524a18db130a
Transactions (2)
Coinbase85315993b58a24…d385085ccc7c5a
1 in β†’ 1 out10.2400 XPM109 B
AUm1UXE6…STx2UrXW
46aec318a779df…06e6b20ee58600
1 in β†’ 2 out6.1525 XPM226 B
ATqt5Krn…uuieYzjNAdWp2YRv…FDtt217a
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.

2.641 Γ— 10⁹³(94-digit number)
26416862801616470874…72179322708985083531
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
2.641 Γ— 10⁹³(94-digit number)
26416862801616470874…72179322708985083531
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.283 Γ— 10⁹³(94-digit number)
52833725603232941749…44358645417970167061
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.056 Γ— 10⁹⁴(95-digit number)
10566745120646588349…88717290835940334121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.113 Γ— 10⁹⁴(95-digit number)
21133490241293176699…77434581671880668241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.226 Γ— 10⁹⁴(95-digit number)
42266980482586353399…54869163343761336481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.453 Γ— 10⁹⁴(95-digit number)
84533960965172706798…09738326687522672961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.690 Γ— 10⁹⁡(96-digit number)
16906792193034541359…19476653375045345921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.381 Γ— 10⁹⁡(96-digit number)
33813584386069082719…38953306750090691841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.762 Γ— 10⁹⁡(96-digit number)
67627168772138165438…77906613500181383681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.352 Γ— 10⁹⁢(97-digit number)
13525433754427633087…55813227000362767361
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:57,655,082 XPMΒ·at block #6,801,375 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