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Block #106,252

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/8/2013, 10:50:26 PM Β· Difficulty 9.6014 Β· 6,700,068 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
208cb65a89a3d412eea7d9fd22e7a7f7a9464a64425acbe12c77f59981a3fe59
View on Chainz β†—

Height

#106,252

Difficulty

9.601402

Transactions

2

Size

391 B

Version

2

Bits

0999f57e

Nonce

168,906

Timestamp

8/8/2013, 10:50:26 PM

Confirmations

6,700,068

Mined by

⛏️ P2SHAYnPP6jGbaP3mcP6f7Y2JYaUgPQ3sS4Pbg

Merkle Root

4a29949ed3d70008523afd5de524173782396348be3d16c2aa485bed4d76ab62
Transactions (2)
Coinbase646874001dc604…aac53f0e17b38c
1 in β†’ 1 out10.8400 XPM109 B
AYnPP6jG…Q3sS4Pbg
dcb444e147b8d7…ac1cc7b4589974
1 in β†’ 1 out199.9900 XPM192 B
AHUbt4Ww…hcxVK8Cp
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.

1.409 Γ— 10⁹⁡(96-digit number)
14092870042339357959…81372099517011832191
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
1.409 Γ— 10⁹⁡(96-digit number)
14092870042339357959…81372099517011832191
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.818 Γ— 10⁹⁡(96-digit number)
28185740084678715918…62744199034023664381
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.637 Γ— 10⁹⁡(96-digit number)
56371480169357431837…25488398068047328761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.127 Γ— 10⁹⁢(97-digit number)
11274296033871486367…50976796136094657521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.254 Γ— 10⁹⁢(97-digit number)
22548592067742972734…01953592272189315041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.509 Γ— 10⁹⁢(97-digit number)
45097184135485945469…03907184544378630081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.019 Γ— 10⁹⁢(97-digit number)
90194368270971890939…07814369088757260161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.803 Γ— 10⁹⁷(98-digit number)
18038873654194378187…15628738177514520321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.607 Γ— 10⁹⁷(98-digit number)
36077747308388756375…31257476355029040641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.215 Γ— 10⁹⁷(98-digit number)
72155494616777512751…62514952710058081281
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,694,642 XPMΒ·at block #6,806,319 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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