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Block #1,856,579

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/19/2016, 2:46:05 PM Β· Difficulty 10.6675 Β· 4,974,466 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7f15872009dc459d01b15cfac8741e70453d8906d89808fada79929f65b847fb
View on Chainz β†—

Height

#1,856,579

Difficulty

10.667458

Transactions

1

Size

243 B

Version

2

Bits

0aaade81

Nonce

259,490,284

Timestamp

11/19/2016, 2:46:05 PM

Confirmations

4,974,466

Mined by

⛏️ P2SHAMeY5ZrV7AqtjFwPLjnwr3BDd53veG96Ko

Merkle Root

53c033449e28cfdaf7cddcb834584b604904a1c5d4f612afc3de031f5a5452ee
Transactions (1)
Coinbase53c033449e28cf…de031f5a5452ee
1 in β†’ 2 out8.7700 XPM152 B
AMeY5ZrV…3veG96KoALPu3s2c…EJXLjVFh
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.

1.431 Γ— 10⁹⁷(98-digit number)
14312755388892357571…47073659438835212799
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
1.431 Γ— 10⁹⁷(98-digit number)
14312755388892357571…47073659438835212799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.862 Γ— 10⁹⁷(98-digit number)
28625510777784715143…94147318877670425599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.725 Γ— 10⁹⁷(98-digit number)
57251021555569430287…88294637755340851199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.145 Γ— 10⁹⁸(99-digit number)
11450204311113886057…76589275510681702399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.290 Γ— 10⁹⁸(99-digit number)
22900408622227772115…53178551021363404799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.580 Γ— 10⁹⁸(99-digit number)
45800817244455544230…06357102042726809599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.160 Γ— 10⁹⁸(99-digit number)
91601634488911088460…12714204085453619199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.832 Γ— 10⁹⁹(100-digit number)
18320326897782217692…25428408170907238399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.664 Γ— 10⁹⁹(100-digit number)
36640653795564435384…50856816341814476799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.328 Γ— 10⁹⁹(100-digit number)
73281307591128870768…01713632683628953599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.465 Γ— 10¹⁰⁰(101-digit number)
14656261518225774153…03427265367257907199
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 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
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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,892,498 XPMΒ·at block #6,831,044 Β· updates every 60s
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