XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,534,528

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/10/2016, 7:33:52 AM Β· Difficulty 10.6168 Β· 5,282,474 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
06c6233f1dffaaa72936dc6921567cf1c22c0c2c92f4f68d9ebc29ea8b5d77ec
View on Chainz β†—

Height

#1,534,528

Difficulty

10.616826

Transactions

2

Size

7.61 KB

Version

2

Bits

0a9de848

Nonce

1,097,268,986

Timestamp

4/10/2016, 7:33:52 AM

Confirmations

5,282,474

Mined by

⛏️ P2SHAM2EWmv8ZBR3Bq4bm2gwwoRAUDy9W6MDAB

Merkle Root

82b3bdfcf7ee0979bd7183612d66c742dd9b58f291f1e00fab0c6f7e8325c653
Transactions (2)
Coinbaseebb2028f5f6e61…d3d6c3275ad5f3
1 in β†’ 1 out8.9400 XPM110 B
AM2EWmv8…y9W6MDAB
a09d05627cb68c…3d0c7b3b6fd4f0
51 in β†’ 1 out1158.4803 XPM7.42 KB
ARuqrf7M…dxyEv85H
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.

1.932 Γ— 10⁹⁷(98-digit number)
19324901010639444126…99347618292650623999
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
1.932 Γ— 10⁹⁷(98-digit number)
19324901010639444126…99347618292650623999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.864 Γ— 10⁹⁷(98-digit number)
38649802021278888252…98695236585301247999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.729 Γ— 10⁹⁷(98-digit number)
77299604042557776505…97390473170602495999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.545 Γ— 10⁹⁸(99-digit number)
15459920808511555301…94780946341204991999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.091 Γ— 10⁹⁸(99-digit number)
30919841617023110602…89561892682409983999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.183 Γ— 10⁹⁸(99-digit number)
61839683234046221204…79123785364819967999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.236 Γ— 10⁹⁹(100-digit number)
12367936646809244240…58247570729639935999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.473 Γ— 10⁹⁹(100-digit number)
24735873293618488481…16495141459279871999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.947 Γ— 10⁹⁹(100-digit number)
49471746587236976963…32990282918559743999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.894 Γ— 10⁹⁹(100-digit number)
98943493174473953927…65980565837119487999
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:57,780,048 XPMΒ·at block #6,817,001 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