XPM Prime Explorer symbol
XPMPrime Explorer

Block #427,617

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/3/2014, 11:03:04 AM Β· Difficulty 10.3522 Β· 6,385,072 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a1f8fffd0ca60da6fbeab43052b16519de3bb06f85b291debb367ed8bd4b7c3c
View on Chainz β†—

Height

#427,617

Difficulty

10.352193

Transactions

2

Size

394 B

Version

2

Bits

0a5a2959

Nonce

7,113

Timestamp

3/3/2014, 11:03:04 AM

Confirmations

6,385,072

Mined by

⛏️ P2SHANNk9YcMfvWEzdGW3MU9gaFDBS9pcnhkwp

Merkle Root

3705cc05b7f9142d452e162ba82c533414f7bf5f49e46e99141763851fc27c35
Transactions (2)
Coinbaseda360d95118637…3a98d00fff8799
1 in β†’ 1 out9.3300 XPM109 B
ANNk9YcM…9pcnhkwp
82964614754dd7…42d93aae8770e2
1 in β†’ 1 out0.0800 XPM192 B
AYouHy4D…Ry7wVgsK
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.

6.230 Γ— 10¹⁰²(103-digit number)
62303979395711113758…64899556736784017281
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
6.230 Γ— 10¹⁰²(103-digit number)
62303979395711113758…64899556736784017281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.246 Γ— 10¹⁰³(104-digit number)
12460795879142222751…29799113473568034561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.492 Γ— 10¹⁰³(104-digit number)
24921591758284445503…59598226947136069121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.984 Γ— 10¹⁰³(104-digit number)
49843183516568891006…19196453894272138241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.968 Γ— 10¹⁰³(104-digit number)
99686367033137782013…38392907788544276481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.993 Γ— 10¹⁰⁴(105-digit number)
19937273406627556402…76785815577088552961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.987 Γ— 10¹⁰⁴(105-digit number)
39874546813255112805…53571631154177105921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.974 Γ— 10¹⁰⁴(105-digit number)
79749093626510225610…07143262308354211841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.594 Γ— 10¹⁰⁡(106-digit number)
15949818725302045122…14286524616708423681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.189 Γ— 10¹⁰⁡(106-digit number)
31899637450604090244…28573049233416847361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.379 Γ— 10¹⁰⁡(106-digit number)
63799274901208180488…57146098466833694721
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,745,547 XPMΒ·at block #6,812,688 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