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Block #901,905

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/19/2015, 10:27:03 PM Β· Difficulty 10.9410 Β· 5,908,231 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
800ecaa610b447f51fa1ea386ede8e25366a19ba2f8dc6ff70788928360270ed
View on Chainz β†—

Height

#901,905

Difficulty

10.940960

Transactions

2

Size

3.75 KB

Version

2

Bits

0af0e2c1

Nonce

516,782,845

Timestamp

1/19/2015, 10:27:03 PM

Confirmations

5,908,231

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

b77d27b31caa6d155ba4ee39cc6b51f0d0efd73ab245e915a93b6adf11630bb6
Transactions (2)
Coinbase6fdb5acc2d1414…47fcd30dfc3e3f
1 in β†’ 1 out8.3800 XPM116 B
ANSXnLY2…Sd25TjkD
d996fb657524cb…5f67b2b21782ef
24 in β†’ 2 out6495.1518 XPM3.54 KB
AccVBCSL…2LBF3eRfANGTb4nb…F8oAXf6g
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.

9.912 Γ— 10⁹⁢(97-digit number)
99122668614914106282…09537274926745742401
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
9.912 Γ— 10⁹⁢(97-digit number)
99122668614914106282…09537274926745742401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.982 Γ— 10⁹⁷(98-digit number)
19824533722982821256…19074549853491484801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.964 Γ— 10⁹⁷(98-digit number)
39649067445965642512…38149099706982969601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.929 Γ— 10⁹⁷(98-digit number)
79298134891931285025…76298199413965939201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.585 Γ— 10⁹⁸(99-digit number)
15859626978386257005…52596398827931878401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.171 Γ— 10⁹⁸(99-digit number)
31719253956772514010…05192797655863756801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.343 Γ— 10⁹⁸(99-digit number)
63438507913545028020…10385595311727513601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.268 Γ— 10⁹⁹(100-digit number)
12687701582709005604…20771190623455027201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.537 Γ— 10⁹⁹(100-digit number)
25375403165418011208…41542381246910054401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.075 Γ— 10⁹⁹(100-digit number)
50750806330836022416…83084762493820108801
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:57,725,155 XPMΒ·at block #6,810,135 Β· updates every 60s
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