XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,151,054

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/11/2015, 9:25:12 PM Β· Difficulty 10.9458 Β· 5,665,030 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
972deec10ec17622bef9482b4df914948eb7255e70d716aa9dd466b926bae7e5
View on Chainz β†—

Height

#1,151,054

Difficulty

10.945841

Transactions

2

Size

581 B

Version

2

Bits

0af222a1

Nonce

297,109,126

Timestamp

7/11/2015, 9:25:12 PM

Confirmations

5,665,030

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

5b9c935dcc60ab95bf712a1aae628bdaf2c0c91cc2c7279502cfb8d9507ee71b
Transactions (2)
Coinbase3e5b222c4e2b6f…a8732d55c5287b
1 in β†’ 1 out8.3500 XPM116 B
AJCEY9yy…tg97E6zm
5c06f202af15f6…4d19eeb49cdd87
2 in β†’ 2 out6.0398 XPM374 B
AHim63Zo…tPm1v8RSAK9LxQQh…h24pctRm
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.

8.590 Γ— 10⁹⁷(98-digit number)
85906616630918178174…76335147775538255361
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
8.590 Γ— 10⁹⁷(98-digit number)
85906616630918178174…76335147775538255361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.718 Γ— 10⁹⁸(99-digit number)
17181323326183635634…52670295551076510721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.436 Γ— 10⁹⁸(99-digit number)
34362646652367271269…05340591102153021441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.872 Γ— 10⁹⁸(99-digit number)
68725293304734542539…10681182204306042881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.374 Γ— 10⁹⁹(100-digit number)
13745058660946908507…21362364408612085761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.749 Γ— 10⁹⁹(100-digit number)
27490117321893817015…42724728817224171521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.498 Γ— 10⁹⁹(100-digit number)
54980234643787634031…85449457634448343041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.099 Γ— 10¹⁰⁰(101-digit number)
10996046928757526806…70898915268896686081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.199 Γ— 10¹⁰⁰(101-digit number)
21992093857515053612…41797830537793372161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.398 Γ— 10¹⁰⁰(101-digit number)
43984187715030107225…83595661075586744321
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:57,772,790 XPMΒ·at block #6,816,083 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