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Block #196,053

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/6/2013, 5:59:04 AM Β· Difficulty 9.8802 Β· 6,611,394 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a151cef2f778c658321bc2e5a8d37d965bdcdf0f0b488fefcc02116441672167
View on Chainz β†—

Height

#196,053

Difficulty

9.880189

Transactions

1

Size

199 B

Version

2

Bits

09e15417

Nonce

24,973

Timestamp

10/6/2013, 5:59:04 AM

Confirmations

6,611,394

Mined by

⛏️ P2SHAKgiTbagke9hfkPB2Na9G5N62UMJA8ujWZ

Merkle Root

e709e3e725f0c624f8cf8e4021f3bcaff667bbdfaf7884acd16f29ee55fde24d
Transactions (1)
Coinbasee709e3e725f0c6…6f29ee55fde24d
1 in β†’ 1 out10.2300 XPM109 B
AKgiTbag…MJA8ujWZ
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.

9.531 Γ— 10⁹³(94-digit number)
95313229440251189047…68591182513071050891
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
9.531 Γ— 10⁹³(94-digit number)
95313229440251189047…68591182513071050891
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.906 Γ— 10⁹⁴(95-digit number)
19062645888050237809…37182365026142101781
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.812 Γ— 10⁹⁴(95-digit number)
38125291776100475618…74364730052284203561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.625 Γ— 10⁹⁴(95-digit number)
76250583552200951237…48729460104568407121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.525 Γ— 10⁹⁡(96-digit number)
15250116710440190247…97458920209136814241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.050 Γ— 10⁹⁡(96-digit number)
30500233420880380495…94917840418273628481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.100 Γ— 10⁹⁡(96-digit number)
61000466841760760990…89835680836547256961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.220 Γ— 10⁹⁢(97-digit number)
12200093368352152198…79671361673094513921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.440 Γ— 10⁹⁢(97-digit number)
24400186736704304396…59342723346189027841
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:57,703,598 XPMΒ·at block #6,807,446 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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