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Block #256,030

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/11/2013, 2:11:47 PM Β· Difficulty 9.9750 Β· 6,561,217 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5c1d257de8deffe32b4b160d3dce5e4fc9544df416f4d73d8b14d2d40cce72b7
View on Chainz β†—

Height

#256,030

Difficulty

9.974979

Transactions

2

Size

425 B

Version

2

Bits

09f9983e

Nonce

3,999

Timestamp

11/11/2013, 2:11:47 PM

Confirmations

6,561,217

Mined by

⛏️ P2SHAXwJx1W1v4BPgTi3pAhA9Tg7X5my2yrEaX

Merkle Root

31bcb54d0be2c3af0d8c9bc780c6a803de511340d3422b7313c03e1908506ea9
Transactions (2)
Coinbase7e630dd6e97c45…1430c7d5d0982c
1 in β†’ 1 out10.0500 XPM109 B
AXwJx1W1…my2yrEaX
d5634e272648b1…0d13d7fd1eb26c
1 in β†’ 2 out5.6384 XPM226 B
AHsWCi12…CCEDAt7yAGyhc9Ym…YqF23X8n
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.

1.364 Γ— 10⁹⁴(95-digit number)
13645494544507206886…15667384698213580801
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
1.364 Γ— 10⁹⁴(95-digit number)
13645494544507206886…15667384698213580801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.729 Γ— 10⁹⁴(95-digit number)
27290989089014413772…31334769396427161601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.458 Γ— 10⁹⁴(95-digit number)
54581978178028827544…62669538792854323201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.091 Γ— 10⁹⁡(96-digit number)
10916395635605765508…25339077585708646401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.183 Γ— 10⁹⁡(96-digit number)
21832791271211531017…50678155171417292801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.366 Γ— 10⁹⁡(96-digit number)
43665582542423062035…01356310342834585601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.733 Γ— 10⁹⁡(96-digit number)
87331165084846124070…02712620685669171201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.746 Γ— 10⁹⁢(97-digit number)
17466233016969224814…05425241371338342401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.493 Γ— 10⁹⁢(97-digit number)
34932466033938449628…10850482742676684801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.986 Γ— 10⁹⁢(97-digit number)
69864932067876899256…21700965485353369601
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:57,782,009 XPMΒ·at block #6,817,246 Β· updates every 60s
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