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Block #29,329

2CCLength 7β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/13/2013, 3:10:42 PM Β· Difficulty 7.9843 Β· 6,781,452 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
677bc7716f0a8ccd172efa3ee0f845a74d2b8a71baad06b30a33a4d67c456b7a
View on Chainz β†—

Height

#29,329

Difficulty

7.984349

Transactions

1

Size

200 B

Version

2

Bits

07fbfe53

Nonce

449

Timestamp

7/13/2013, 3:10:42 PM

Confirmations

6,781,452

Mined by

⛏️ P2SHAV3Mx3AqCBr85EUqewYnyDKYAdAKiwER2W

Merkle Root

b050895ece008bd4781ce0cd53d5ac24fdcf460fcf613407a61ef923b8fbc3e0
Transactions (1)
Coinbaseb050895ece008b…1ef923b8fbc3e0
1 in β†’ 1 out15.6700 XPM109 B
AV3Mx3Aq…AKiwER2W
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.

8.124 Γ— 10⁹⁡(96-digit number)
81249571564353629078…27535495034285244801
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
8.124 Γ— 10⁹⁡(96-digit number)
81249571564353629078…27535495034285244801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.624 Γ— 10⁹⁢(97-digit number)
16249914312870725815…55070990068570489601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.249 Γ— 10⁹⁢(97-digit number)
32499828625741451631…10141980137140979201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.499 Γ— 10⁹⁢(97-digit number)
64999657251482903263…20283960274281958401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.299 Γ— 10⁹⁷(98-digit number)
12999931450296580652…40567920548563916801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.599 Γ— 10⁹⁷(98-digit number)
25999862900593161305…81135841097127833601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.199 Γ— 10⁹⁷(98-digit number)
51999725801186322610…62271682194255667201
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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 7

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:57,730,344 XPMΒ·at block #6,810,780 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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