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Block #862,095

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/21/2014, 11:43:36 AM Β· Difficulty 10.9637 Β· 5,964,896 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
385196e7e95f7c05dfc3706e9c8741f08ca8ff2faec6e516f297b250065f4aaf
View on Chainz β†—

Height

#862,095

Difficulty

10.963665

Transactions

2

Size

27.00 KB

Version

2

Bits

0af6b2c3

Nonce

120,884,549

Timestamp

12/21/2014, 11:43:36 AM

Confirmations

5,964,896

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

26748eb9ea6680ab72469b408460da65a58c826f54dd7076d448e4d955d32f86
Transactions (2)
Coinbasee3e057d974163d…5fc902839d0317
1 in β†’ 1 out8.6400 XPM116 B
ANSXnLY2…Sd25TjkD
7e3cf84d5a5e86…1533f235f79f60
185 in β†’ 2 out3.6282 XPM26.80 KB
AZvWpKVn…hR8af2caAT12DE6t…49WcEEBP
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.

2.533 Γ— 10⁹⁡(96-digit number)
25338566743038940915…51291073251751137281
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
2.533 Γ— 10⁹⁡(96-digit number)
25338566743038940915…51291073251751137281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.067 Γ— 10⁹⁡(96-digit number)
50677133486077881831…02582146503502274561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.013 Γ— 10⁹⁢(97-digit number)
10135426697215576366…05164293007004549121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.027 Γ— 10⁹⁢(97-digit number)
20270853394431152732…10328586014009098241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.054 Γ— 10⁹⁢(97-digit number)
40541706788862305465…20657172028018196481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.108 Γ— 10⁹⁢(97-digit number)
81083413577724610930…41314344056036392961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.621 Γ— 10⁹⁷(98-digit number)
16216682715544922186…82628688112072785921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.243 Γ— 10⁹⁷(98-digit number)
32433365431089844372…65257376224145571841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.486 Γ— 10⁹⁷(98-digit number)
64866730862179688744…30514752448291143681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.297 Γ— 10⁹⁸(99-digit number)
12973346172435937748…61029504896582287361
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:57,860,103 XPMΒ·at block #6,826,990 Β· updates every 60s
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