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Block #188,783

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/1/2013, 10:02:06 AM Β· Difficulty 9.8712 Β· 6,619,441 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a411b0079d870cb043acd0951708b3e33833b379c5b59877350b85a4c1ec015e
View on Chainz β†—

Height

#188,783

Difficulty

9.871168

Transactions

2

Size

572 B

Version

2

Bits

09df04e1

Nonce

12,454

Timestamp

10/1/2013, 10:02:06 AM

Confirmations

6,619,441

Mined by

⛏️ P2SHAVQtj9szcPSbXf2Kn31DQ2okAd4P34aCDq

Merkle Root

f8fb4cc5abb19709ac32148547d85e1989dae736dc6c989b6831eff60c8a7991
Transactions (2)
Coinbase7f3b5ef1a75075…b12c50b4f43a37
1 in β†’ 1 out10.2600 XPM109 B
AVQtj9sz…4P34aCDq
e6c9a1f5ac219d…a35c8812a0165e
2 in β†’ 2 out6.0218 XPM373 B
AXfCh7p7…WU5Gj3hjAVE9fGQr…5oL1hYv6
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.

6.502 Γ— 10⁹⁡(96-digit number)
65020237285762136152…25142851412604906601
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
6.502 Γ— 10⁹⁡(96-digit number)
65020237285762136152…25142851412604906601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.300 Γ— 10⁹⁢(97-digit number)
13004047457152427230…50285702825209813201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.600 Γ— 10⁹⁢(97-digit number)
26008094914304854460…00571405650419626401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.201 Γ— 10⁹⁢(97-digit number)
52016189828609708921…01142811300839252801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.040 Γ— 10⁹⁷(98-digit number)
10403237965721941784…02285622601678505601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.080 Γ— 10⁹⁷(98-digit number)
20806475931443883568…04571245203357011201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.161 Γ— 10⁹⁷(98-digit number)
41612951862887767137…09142490406714022401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.322 Γ— 10⁹⁷(98-digit number)
83225903725775534274…18284980813428044801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.664 Γ— 10⁹⁸(99-digit number)
16645180745155106854…36569961626856089601
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:57,709,844 XPMΒ·at block #6,808,223 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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