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Block #134,013

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/25/2013, 8:13:00 PM Β· Difficulty 9.7995 Β· 6,683,086 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ab884b5e10e019c74aafd8152c2184129bcaaeb5623ba96fd3d4d50b4660a224
View on Chainz β†—

Height

#134,013

Difficulty

9.799550

Transactions

1

Size

199 B

Version

2

Bits

09ccaf4b

Nonce

99,822

Timestamp

8/25/2013, 8:13:00 PM

Confirmations

6,683,086

Mined by

⛏️ P2SHAY88KHSTJpyaPqTYGEt3LWdPpt88L8yacq

Merkle Root

ba8a52a598743b9ce4114cb6c25999df59382fa12074343f8a95afddcd2d326b
Transactions (1)
Coinbaseba8a52a598743b…95afddcd2d326b
1 in β†’ 1 out10.4000 XPM109 B
AY88KHST…88L8yacq
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.

5.230 Γ— 10⁹⁴(95-digit number)
52303741141652622747…13724625942145431681
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
5.230 Γ— 10⁹⁴(95-digit number)
52303741141652622747…13724625942145431681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.046 Γ— 10⁹⁡(96-digit number)
10460748228330524549…27449251884290863361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.092 Γ— 10⁹⁡(96-digit number)
20921496456661049099…54898503768581726721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.184 Γ— 10⁹⁡(96-digit number)
41842992913322098198…09797007537163453441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.368 Γ— 10⁹⁡(96-digit number)
83685985826644196396…19594015074326906881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.673 Γ— 10⁹⁢(97-digit number)
16737197165328839279…39188030148653813761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.347 Γ— 10⁹⁢(97-digit number)
33474394330657678558…78376060297307627521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.694 Γ— 10⁹⁢(97-digit number)
66948788661315357117…56752120594615255041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.338 Γ— 10⁹⁷(98-digit number)
13389757732263071423…13504241189230510081
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
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