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Block #134,341

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/26/2013, 12:11:01 AM Β· Difficulty 9.8031 Β· 6,675,512 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
66d7c81a44edcb52a4bce31fd483b41ef31b876755714b98e5cdaa55def60e67
View on Chainz β†—

Height

#134,341

Difficulty

9.803102

Transactions

1

Size

198 B

Version

2

Bits

09cd9815

Nonce

26,558

Timestamp

8/26/2013, 12:11:01 AM

Confirmations

6,675,512

Mined by

⛏️ P2SHAcecj4WYP2kTRjXJMUTPed41WTwKtCNbS5

Merkle Root

0e6efd49cfd9fd21f3077d72533ea49c950103ae7101c253f55a1c5b85cc3bf3
Transactions (1)
Coinbase0e6efd49cfd9fd…5a1c5b85cc3bf3
1 in β†’ 1 out10.3900 XPM109 B
Acecj4WY…wKtCNbS5
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.

8.510 Γ— 10⁹²(93-digit number)
85108693987972200039…13964615076176712961
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
8.510 Γ— 10⁹²(93-digit number)
85108693987972200039…13964615076176712961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.702 Γ— 10⁹³(94-digit number)
17021738797594440007…27929230152353425921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.404 Γ— 10⁹³(94-digit number)
34043477595188880015…55858460304706851841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.808 Γ— 10⁹³(94-digit number)
68086955190377760031…11716920609413703681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.361 Γ— 10⁹⁴(95-digit number)
13617391038075552006…23433841218827407361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.723 Γ— 10⁹⁴(95-digit number)
27234782076151104012…46867682437654814721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.446 Γ— 10⁹⁴(95-digit number)
54469564152302208025…93735364875309629441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.089 Γ— 10⁹⁡(96-digit number)
10893912830460441605…87470729750619258881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.178 Γ— 10⁹⁡(96-digit number)
21787825660920883210…74941459501238517761
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:57,722,911 XPMΒ·at block #6,809,852 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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