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Block #103,501

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/7/2013, 3:15:31 PM Β· Difficulty 9.5272 Β· 6,695,817 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d593d2fd6bfc3c67d4619c8aab3ccb71e4f0d2517f2df1f95a192dff3fc56f47
View on Chainz β†—

Height

#103,501

Difficulty

9.527245

Transactions

1

Size

198 B

Version

2

Bits

0986f988

Nonce

9,094

Timestamp

8/7/2013, 3:15:31 PM

Confirmations

6,695,817

Mined by

⛏️ P2SHAPMtWWMVeVGtTuzxX7wwtVneQMfSBBhpZA

Merkle Root

be634f4cd40231b69979ba6964720491d186a95bc6aa007bd77df3d634d6f41b
Transactions (1)
Coinbasebe634f4cd40231…7df3d634d6f41b
1 in β†’ 1 out11.0000 XPM109 B
APMtWWMV…fSBBhpZA
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.

5.733 Γ— 10⁹²(93-digit number)
57333204604293125878…19968491003776843601
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
5.733 Γ— 10⁹²(93-digit number)
57333204604293125878…19968491003776843601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.146 Γ— 10⁹³(94-digit number)
11466640920858625175…39936982007553687201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.293 Γ— 10⁹³(94-digit number)
22933281841717250351…79873964015107374401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.586 Γ— 10⁹³(94-digit number)
45866563683434500703…59747928030214748801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.173 Γ— 10⁹³(94-digit number)
91733127366869001406…19495856060429497601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.834 Γ— 10⁹⁴(95-digit number)
18346625473373800281…38991712120858995201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.669 Γ— 10⁹⁴(95-digit number)
36693250946747600562…77983424241717990401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.338 Γ— 10⁹⁴(95-digit number)
73386501893495201124…55966848483435980801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.467 Γ— 10⁹⁡(96-digit number)
14677300378699040224…11933696966871961601
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,638,592 XPMΒ·at block #6,799,317 Β· updates every 60s
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