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Block #89,029

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/30/2013, 1:49:17 AM Β· Difficulty 9.2618 Β· 6,719,048 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c3ee7f6e152dac4e1ee654d48bdcb4ff70da190a1d3989fc01375ee3a5dd0c7f
View on Chainz β†—

Height

#89,029

Difficulty

9.261838

Transactions

1

Size

201 B

Version

2

Bits

094307d6

Nonce

492

Timestamp

7/30/2013, 1:49:17 AM

Confirmations

6,719,048

Mined by

⛏️ P2SHAeyq3v5jMQ3ugf3cSfyfKJZbx8UBA8Mxcy

Merkle Root

3a7babe1116445309a90a3646d95786c977b5df7260c71f0af912cc75c4cfc28
Transactions (1)
Coinbase3a7babe1116445…912cc75c4cfc28
1 in β†’ 1 out11.6400 XPM110 B
Aeyq3v5j…UBA8Mxcy
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.

3.579 Γ— 10⁹⁢(97-digit number)
35791067722980258651…38334186459673697461
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
3.579 Γ— 10⁹⁢(97-digit number)
35791067722980258651…38334186459673697461
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.158 Γ— 10⁹⁢(97-digit number)
71582135445960517302…76668372919347394921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.431 Γ— 10⁹⁷(98-digit number)
14316427089192103460…53336745838694789841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.863 Γ— 10⁹⁷(98-digit number)
28632854178384206921…06673491677389579681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.726 Γ— 10⁹⁷(98-digit number)
57265708356768413842…13346983354779159361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.145 Γ— 10⁹⁸(99-digit number)
11453141671353682768…26693966709558318721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.290 Γ— 10⁹⁸(99-digit number)
22906283342707365536…53387933419116637441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.581 Γ— 10⁹⁸(99-digit number)
45812566685414731073…06775866838233274881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.162 Γ— 10⁹⁸(99-digit number)
91625133370829462147…13551733676466549761
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:57,708,663 XPMΒ·at block #6,808,076 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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