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Block #1,235,421

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/13/2015, 9:18:31 PM Β· Difficulty 10.7525 Β· 5,559,230 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5a29b6fb5e72af48796ccaa61bff63da7b7d3ca7f4d39c97c870151ce6553915
View on Chainz β†—

Height

#1,235,421

Difficulty

10.752520

Transactions

3

Size

650 B

Version

2

Bits

0ac0a523

Nonce

728,290,946

Timestamp

9/13/2015, 9:18:31 PM

Confirmations

5,559,230

Mined by

⛏️ P2SHATr96xTZA1srCjUxdxvMjh8D48Hwy3Cc6e

Merkle Root

621966133dfe2a7121968c601b3afce60b8cb9e5a0242581f71df8781b0d7ac3
Transactions (3)
Coinbasee961c2e0090d76…d73d14a0301a8c
1 in β†’ 1 out8.6600 XPM109 B
ATr96xTZ…Hwy3Cc6e
13257b36d1f82b…c2bb944fb81123
1 in β†’ 2 out8.6400 XPM226 B
AVtH48GT…4NZmxKtAAX4WQ8Gn…4nCZtmpL
6deeaab2ff332b…f9e9127a2aea36
1 in β†’ 2 out8.6400 XPM225 B
AXrTw46X…e1dGvSFfAL6AjcR8…ocrn6uSk
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.

5.755 Γ— 10⁹³(94-digit number)
57555238596661619864…48415269255470359041
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
5.755 Γ— 10⁹³(94-digit number)
57555238596661619864…48415269255470359041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.151 Γ— 10⁹⁴(95-digit number)
11511047719332323972…96830538510940718081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.302 Γ— 10⁹⁴(95-digit number)
23022095438664647945…93661077021881436161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.604 Γ— 10⁹⁴(95-digit number)
46044190877329295891…87322154043762872321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.208 Γ— 10⁹⁴(95-digit number)
92088381754658591783…74644308087525744641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.841 Γ— 10⁹⁡(96-digit number)
18417676350931718356…49288616175051489281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.683 Γ— 10⁹⁡(96-digit number)
36835352701863436713…98577232350102978561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.367 Γ— 10⁹⁡(96-digit number)
73670705403726873426…97154464700205957121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.473 Γ— 10⁹⁢(97-digit number)
14734141080745374685…94308929400411914241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.946 Γ— 10⁹⁢(97-digit number)
29468282161490749370…88617858800823828481
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:57,601,257 XPMΒ·at block #6,794,650 Β· updates every 60s
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