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Block #1,969,950

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/5/2017, 9:08:15 AM Β· Difficulty 10.7516 Β· 4,833,207 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0e5456de13023f9a50d1b2ac62d81c2c8864eba0e78fc1d2705df266debef476
View on Chainz β†—

Height

#1,969,950

Difficulty

10.751569

Transactions

1

Size

199 B

Version

2

Bits

0ac066d5

Nonce

427

Timestamp

2/5/2017, 9:08:15 AM

Confirmations

4,833,207

Mined by

⛏️ P2SHAYc3QGYaSv1sA3FuuZuBoiE4ttSWDuszQp

Merkle Root

7f2d415446f247232b64c6f26fd2b56831d491149db6f48d31a4af4845fe3f1b
Transactions (1)
Coinbase7f2d415446f247…a4af4845fe3f1b
1 in β†’ 1 out8.6400 XPM109 B
AYc3QGYa…SWDuszQp
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.

7.709 Γ— 10⁹³(94-digit number)
77090274326229839327…97640244509886903121
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
7.709 Γ— 10⁹³(94-digit number)
77090274326229839327…97640244509886903121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.541 Γ— 10⁹⁴(95-digit number)
15418054865245967865…95280489019773806241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.083 Γ— 10⁹⁴(95-digit number)
30836109730491935731…90560978039547612481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.167 Γ— 10⁹⁴(95-digit number)
61672219460983871462…81121956079095224961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.233 Γ— 10⁹⁡(96-digit number)
12334443892196774292…62243912158190449921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.466 Γ— 10⁹⁡(96-digit number)
24668887784393548584…24487824316380899841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.933 Γ— 10⁹⁡(96-digit number)
49337775568787097169…48975648632761799681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.867 Γ— 10⁹⁡(96-digit number)
98675551137574194339…97951297265523599361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.973 Γ— 10⁹⁢(97-digit number)
19735110227514838867…95902594531047198721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.947 Γ— 10⁹⁢(97-digit number)
39470220455029677735…91805189062094397441
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:57,669,271 XPMΒ·at block #6,803,156 Β· updates every 60s
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