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Block #270,462

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/23/2013, 11:23:23 PM Β· Difficulty 9.9517 Β· 6,539,674 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ad199f9a6528424cac3069c112d8552b070b06a93e594f35281c4fa47409026e
View on Chainz β†—

Height

#270,462

Difficulty

9.951653

Transactions

2

Size

539 B

Version

2

Bits

09f39f84

Nonce

146,699

Timestamp

11/23/2013, 11:23:23 PM

Confirmations

6,539,674

Mined by

⛏️ P2SHANQnFDz39QSUfineSyrcmiN5nsPStL9hX5

Merkle Root

3d030f080b860cdd674c74b16711357993864fb4b9db59647ce24a2174a809d6
Transactions (2)
Coinbase7e1a4b63932e01…bf0d1f99de1c79
1 in β†’ 1 out10.0900 XPM109 B
ANQnFDz3…PStL9hX5
7615451e1e7dde…53d86ec311d725
2 in β†’ 1 out3.1704 XPM340 B
AVxRAFUd…ivfKAeZQ
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.

1.478 Γ— 10⁹⁴(95-digit number)
14780810570566599376…41556348018163999361
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
1.478 Γ— 10⁹⁴(95-digit number)
14780810570566599376…41556348018163999361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.956 Γ— 10⁹⁴(95-digit number)
29561621141133198752…83112696036327998721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.912 Γ— 10⁹⁴(95-digit number)
59123242282266397505…66225392072655997441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.182 Γ— 10⁹⁡(96-digit number)
11824648456453279501…32450784145311994881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.364 Γ— 10⁹⁡(96-digit number)
23649296912906559002…64901568290623989761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.729 Γ— 10⁹⁡(96-digit number)
47298593825813118004…29803136581247979521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.459 Γ— 10⁹⁡(96-digit number)
94597187651626236008…59606273162495959041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.891 Γ— 10⁹⁢(97-digit number)
18919437530325247201…19212546324991918081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.783 Γ— 10⁹⁢(97-digit number)
37838875060650494403…38425092649983836161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.567 Γ— 10⁹⁢(97-digit number)
75677750121300988806…76850185299967672321
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:57,725,155 XPMΒ·at block #6,810,135 Β· updates every 60s
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