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Block #29,627

2CCLength 7β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/13/2013, 4:10:33 PM Β· Difficulty 7.9851 Β· 6,787,657 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ab6b9d58689447c3326d4a714475c2670a6cc415b7f97644bd04f3180eeb52e4
View on Chainz β†—

Height

#29,627

Difficulty

7.985079

Transactions

1

Size

198 B

Version

2

Bits

07fc2e1f

Nonce

1,260

Timestamp

7/13/2013, 4:10:33 PM

Confirmations

6,787,657

Mined by

⛏️ P2SHASbRxSSzrfffuPGcuJ6s3bNYQdH5rkdjdH

Merkle Root

9209256a8736b0009ce0c5c89305b717c878ca36621fc3224a30e84be0e75b65
Transactions (1)
Coinbase9209256a8736b0…30e84be0e75b65
1 in β†’ 1 out15.6600 XPM108 B
ASbRxSSz…H5rkdjdH
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.

3.980 Γ— 10⁹⁴(95-digit number)
39801700121918345389…42150888412795429761
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
3.980 Γ— 10⁹⁴(95-digit number)
39801700121918345389…42150888412795429761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.960 Γ— 10⁹⁴(95-digit number)
79603400243836690779…84301776825590859521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.592 Γ— 10⁹⁡(96-digit number)
15920680048767338155…68603553651181719041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.184 Γ— 10⁹⁡(96-digit number)
31841360097534676311…37207107302363438081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.368 Γ— 10⁹⁡(96-digit number)
63682720195069352623…74414214604726876161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.273 Γ— 10⁹⁢(97-digit number)
12736544039013870524…48828429209453752321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.547 Γ— 10⁹⁢(97-digit number)
25473088078027741049…97656858418907504641
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:57,782,312 XPMΒ·at block #6,817,283 Β· updates every 60s
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