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Block #884,075

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/6/2015, 6:28:55 AM Β· Difficulty 10.9586 Β· 5,933,413 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b7ec12a96307c8ed23fb7acf5b306577abdf3a90e61b7d8362a40398ebb92ce7
View on Chainz β†—

Height

#884,075

Difficulty

10.958624

Transactions

2

Size

10.83 KB

Version

2

Bits

0af56861

Nonce

220,248,734

Timestamp

1/6/2015, 6:28:55 AM

Confirmations

5,933,413

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

01f1f7c84be2f86aa31d9af8d7dc87a2e367bb1d7a23657e489b57e59850d617
Transactions (2)
Coinbase579eeee17c045e…f48314426a96d2
1 in β†’ 1 out8.4300 XPM116 B
ANSXnLY2…Sd25TjkD
ca6435ef283269…1097e55d3bad95
73 in β†’ 2 out500.1398 XPM10.63 KB
ARUsUACf…1cX9XMtAAJjnK9uC…VreFquR4
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.

5.120 Γ— 10⁹⁡(96-digit number)
51207050066770791960…45751387316004724961
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
5.120 Γ— 10⁹⁡(96-digit number)
51207050066770791960…45751387316004724961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.024 Γ— 10⁹⁢(97-digit number)
10241410013354158392…91502774632009449921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.048 Γ— 10⁹⁢(97-digit number)
20482820026708316784…83005549264018899841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.096 Γ— 10⁹⁢(97-digit number)
40965640053416633568…66011098528037799681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.193 Γ— 10⁹⁢(97-digit number)
81931280106833267136…32022197056075599361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.638 Γ— 10⁹⁷(98-digit number)
16386256021366653427…64044394112151198721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.277 Γ— 10⁹⁷(98-digit number)
32772512042733306854…28088788224302397441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.554 Γ— 10⁹⁷(98-digit number)
65545024085466613709…56177576448604794881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.310 Γ— 10⁹⁸(99-digit number)
13109004817093322741…12355152897209589761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.621 Γ— 10⁹⁸(99-digit number)
26218009634186645483…24710305794419179521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.243 Γ— 10⁹⁸(99-digit number)
52436019268373290967…49420611588838359041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
1.048 Γ— 10⁹⁹(100-digit number)
10487203853674658193…98841223177676718081
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,783,959 XPMΒ·at block #6,817,487 Β· updates every 60s
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