XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,565,438

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/30/2016, 5:56:33 AM Β· Difficulty 10.7536 Β· 5,244,629 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b70445846f3baacb695ba667fea51800f5f83c40afbc4896cf27f5c3b6d5ef7b
View on Chainz β†—

Height

#1,565,438

Difficulty

10.753604

Transactions

1

Size

203 B

Version

2

Bits

0ac0ec2b

Nonce

46,613

Timestamp

4/30/2016, 5:56:33 AM

Confirmations

5,244,629

Mined by

⛏️ P2SHAddPxoMXBQQyF3UwDFeHLzbttJLJ9QJdVK

Merkle Root

454af3d578dad6bad509349559000bf6eefc600f2f5c5605bbb7bd7dbdba5b76
Transactions (1)
Coinbase454af3d578dad6…b7bd7dbdba5b76
1 in β†’ 1 out8.6300 XPM109 B
AddPxoMX…LJ9QJdVK
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.

2.938 Γ— 10¹⁰⁴(105-digit number)
29381662435941034706…25806561117851665119
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
2.938 Γ— 10¹⁰⁴(105-digit number)
29381662435941034706…25806561117851665119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.876 Γ— 10¹⁰⁴(105-digit number)
58763324871882069413…51613122235703330239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.175 Γ— 10¹⁰⁡(106-digit number)
11752664974376413882…03226244471406660479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.350 Γ— 10¹⁰⁡(106-digit number)
23505329948752827765…06452488942813320959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.701 Γ— 10¹⁰⁡(106-digit number)
47010659897505655530…12904977885626641919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.402 Γ— 10¹⁰⁡(106-digit number)
94021319795011311061…25809955771253283839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.880 Γ— 10¹⁰⁢(107-digit number)
18804263959002262212…51619911542506567679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.760 Γ— 10¹⁰⁢(107-digit number)
37608527918004524424…03239823085013135359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.521 Γ— 10¹⁰⁢(107-digit number)
75217055836009048849…06479646170026270719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.504 Γ— 10¹⁰⁷(108-digit number)
15043411167201809769…12959292340052541439
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:57,724,608 XPMΒ·at block #6,810,066 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