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Block #112,967

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/12/2013, 6:54:00 AM Β· Difficulty 9.7274 Β· 6,685,785 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
86e6daa5518fbf0d5f074334c22aff842a4afb2f4c5412683dfb246d7d7f92c6
View on Chainz β†—

Height

#112,967

Difficulty

9.727437

Transactions

2

Size

720 B

Version

2

Bits

09ba3958

Nonce

350,581

Timestamp

8/12/2013, 6:54:00 AM

Confirmations

6,685,785

Mined by

⛏️ P2SHAMRfZY9RXmAjjoBgXZQr53mia6FD9e5E3w

Merkle Root

27df9f8bc7baa16889ed4c4e8889d6f4567954798f0742a209ec1792b3834c77
Transactions (2)
Coinbase12e843ebb6d5d6…13ffd54154156a
1 in β†’ 1 out10.5600 XPM109 B
AMRfZY9R…FD9e5E3w
47227b3a6288a8…da8d22fba12788
3 in β†’ 2 out203.1036 XPM521 B
ANASH7Yw…kjTsgvt1AGFKxejs…o4W8h3Ci
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.

2.490 Γ— 10⁹⁴(95-digit number)
24905772556175544630…09838192435254765531
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
2.490 Γ— 10⁹⁴(95-digit number)
24905772556175544630…09838192435254765531
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.981 Γ— 10⁹⁴(95-digit number)
49811545112351089260…19676384870509531061
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.962 Γ— 10⁹⁴(95-digit number)
99623090224702178521…39352769741019062121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.992 Γ— 10⁹⁡(96-digit number)
19924618044940435704…78705539482038124241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.984 Γ— 10⁹⁡(96-digit number)
39849236089880871408…57411078964076248481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.969 Γ— 10⁹⁡(96-digit number)
79698472179761742816…14822157928152496961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.593 Γ— 10⁹⁢(97-digit number)
15939694435952348563…29644315856304993921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.187 Γ— 10⁹⁢(97-digit number)
31879388871904697126…59288631712609987841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.375 Γ— 10⁹⁢(97-digit number)
63758777743809394253…18577263425219975681
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:57,634,041 XPMΒ·at block #6,798,751 Β· updates every 60s
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