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Block #252,856

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/9/2013, 7:32:25 PM Β· Difficulty 9.9716 Β· 6,554,051 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8d1f6d37daf4aa7e6b9c6846175a316a0943160f78f31f80b11a88ac6be88f63
View on Chainz β†—

Height

#252,856

Difficulty

9.971630

Transactions

1

Size

199 B

Version

2

Bits

09f8bcbb

Nonce

46,630

Timestamp

11/9/2013, 7:32:25 PM

Confirmations

6,554,051

Mined by

⛏️ P2SHAQ4KuZ2UkkCs8rHce3kHkL7Wmf1UKD59gi

Merkle Root

43a51fc8d73e9c979604d543708a114a32cfdc2530385212be65d198960c169a
Transactions (1)
Coinbase43a51fc8d73e9c…65d198960c169a
1 in β†’ 1 out10.0400 XPM109 B
AQ4KuZ2U…1UKD59gi
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.

8.452 Γ— 10⁹⁴(95-digit number)
84520980423132051097…22905771105694731841
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
8.452 Γ— 10⁹⁴(95-digit number)
84520980423132051097…22905771105694731841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.690 Γ— 10⁹⁡(96-digit number)
16904196084626410219…45811542211389463681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.380 Γ— 10⁹⁡(96-digit number)
33808392169252820439…91623084422778927361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.761 Γ— 10⁹⁡(96-digit number)
67616784338505640878…83246168845557854721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.352 Γ— 10⁹⁢(97-digit number)
13523356867701128175…66492337691115709441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.704 Γ— 10⁹⁢(97-digit number)
27046713735402256351…32984675382231418881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.409 Γ— 10⁹⁢(97-digit number)
54093427470804512702…65969350764462837761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.081 Γ— 10⁹⁷(98-digit number)
10818685494160902540…31938701528925675521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.163 Γ— 10⁹⁷(98-digit number)
21637370988321805081…63877403057851351041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.327 Γ— 10⁹⁷(98-digit number)
43274741976643610162…27754806115702702081
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:57,699,366 XPMΒ·at block #6,806,906 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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