XPM Prime Explorer symbol
XPMPrime Explorer

Block #650,782

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/27/2014, 8:20:56 PM Β· Difficulty 10.9529 Β· 6,152,846 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5ae507f5b1587b6f44c095e71b88c217df55b603bbe546354f0100751be41267
View on Chainz β†—

Height

#650,782

Difficulty

10.952919

Transactions

2

Size

68.74 KB

Version

2

Bits

0af3f281

Nonce

471,573,885

Timestamp

7/27/2014, 8:20:56 PM

Confirmations

6,152,846

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

c7f53c926f2fde8a690269c239a241aa27741d89a758025a48540d265294f6d8
Transactions (2)
Coinbase89273d17eadbe3…6e5e1f4a8e770e
1 in β†’ 1 out9.0500 XPM116 B
ANSXnLY2…Sd25TjkD
29deb443b4c33c…aefcd892b1027c
474 in β†’ 1 out1496.1824 XPM68.53 KB
AM2VvvW9…FiFGXpMG
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.

3.003 Γ— 10⁹⁢(97-digit number)
30030136385540068684…86700279448913656321
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
3.003 Γ— 10⁹⁢(97-digit number)
30030136385540068684…86700279448913656321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.006 Γ— 10⁹⁢(97-digit number)
60060272771080137369…73400558897827312641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.201 Γ— 10⁹⁷(98-digit number)
12012054554216027473…46801117795654625281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.402 Γ— 10⁹⁷(98-digit number)
24024109108432054947…93602235591309250561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.804 Γ— 10⁹⁷(98-digit number)
48048218216864109895…87204471182618501121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.609 Γ— 10⁹⁷(98-digit number)
96096436433728219791…74408942365237002241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.921 Γ— 10⁹⁸(99-digit number)
19219287286745643958…48817884730474004481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.843 Γ— 10⁹⁸(99-digit number)
38438574573491287916…97635769460948008961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.687 Γ— 10⁹⁸(99-digit number)
76877149146982575833…95271538921896017921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.537 Γ— 10⁹⁹(100-digit number)
15375429829396515166…90543077843792035841
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:57,673,056 XPMΒ·at block #6,803,627 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