XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,717,572

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/15/2016, 1:02:44 AM Β· Difficulty 10.6646 Β· 5,092,186 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
15108e773feb16c03922a03ed5820d3761aa9920980019130371bdb59850de26
View on Chainz β†—

Height

#1,717,572

Difficulty

10.664615

Transactions

2

Size

426 B

Version

2

Bits

0aaa243a

Nonce

1,198,059,053

Timestamp

8/15/2016, 1:02:44 AM

Confirmations

5,092,186

Mined by

⛏️ P2SHAZGfyv3exuzokuyZ7QFfUHDzMoFa7fw9ZU

Merkle Root

d2ef2d5e195e93548adf9b36d707e7a80f03de59108051c1fd5c3a2dffd06fd0
Transactions (2)
Coinbase2544870f6c379c…1ab013aae96cfe
1 in β†’ 1 out8.7900 XPM110 B
AZGfyv3e…Fa7fw9ZU
a3dea99e5199de…37d5f23a541cb8
1 in β†’ 2 out1317.8986 XPM225 B
AdJF6c71…CWoS2V1UAU5w1QW1…Dprsgm6P
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.

1.260 Γ— 10⁹⁢(97-digit number)
12609696088096959930…40607506220663377919
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.260 Γ— 10⁹⁢(97-digit number)
12609696088096959930…40607506220663377919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.521 Γ— 10⁹⁢(97-digit number)
25219392176193919861…81215012441326755839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.043 Γ— 10⁹⁢(97-digit number)
50438784352387839722…62430024882653511679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.008 Γ— 10⁹⁷(98-digit number)
10087756870477567944…24860049765307023359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.017 Γ— 10⁹⁷(98-digit number)
20175513740955135888…49720099530614046719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.035 Γ— 10⁹⁷(98-digit number)
40351027481910271777…99440199061228093439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.070 Γ— 10⁹⁷(98-digit number)
80702054963820543555…98880398122456186879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.614 Γ— 10⁹⁸(99-digit number)
16140410992764108711…97760796244912373759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.228 Γ— 10⁹⁸(99-digit number)
32280821985528217422…95521592489824747519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.456 Γ— 10⁹⁸(99-digit number)
64561643971056434844…91043184979649495039
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,722,150 XPMΒ·at block #6,809,757 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