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Block #1,354,658

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/4/2015, 9:46:47 PM Β· Difficulty 10.8068 Β· 5,463,161 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4b5ebf83ba875c5c1b8dc31b3cbb78a006148fb6675462367683d0c3f7758f88
View on Chainz β†—

Height

#1,354,658

Difficulty

10.806787

Transactions

2

Size

426 B

Version

2

Bits

0ace899a

Nonce

115,800,359

Timestamp

12/4/2015, 9:46:47 PM

Confirmations

5,463,161

Mined by

⛏️ P2SHAQMD476DteCpAyxn1b9mT7xP7BZbpVYjTX

Merkle Root

e0cbf0978c228786cd98dd68d9939f96f9e9a5dfa89759934dcaee0e564da531
Transactions (2)
Coinbased7d09b5b60b3f6…893523b3f84aa1
1 in β†’ 1 out8.5600 XPM109 B
AQMD476D…ZbpVYjTX
e2ceb1ba3a5ff8…c40f07e9214b0e
1 in β†’ 2 out3.7176 XPM226 B
AcuM7XiJ…5uND8JceAQjmmE2a…7WMDoErh
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.

1.482 Γ— 10⁹⁢(97-digit number)
14826481030094684718…49313592564605113921
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
1.482 Γ— 10⁹⁢(97-digit number)
14826481030094684718…49313592564605113921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.965 Γ— 10⁹⁢(97-digit number)
29652962060189369436…98627185129210227841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.930 Γ— 10⁹⁢(97-digit number)
59305924120378738873…97254370258420455681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.186 Γ— 10⁹⁷(98-digit number)
11861184824075747774…94508740516840911361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.372 Γ— 10⁹⁷(98-digit number)
23722369648151495549…89017481033681822721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.744 Γ— 10⁹⁷(98-digit number)
47444739296302991099…78034962067363645441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.488 Γ— 10⁹⁷(98-digit number)
94889478592605982198…56069924134727290881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.897 Γ— 10⁹⁸(99-digit number)
18977895718521196439…12139848269454581761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.795 Γ— 10⁹⁸(99-digit number)
37955791437042392879…24279696538909163521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.591 Γ— 10⁹⁸(99-digit number)
75911582874084785758…48559393077818327041
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:57,786,615 XPMΒ·at block #6,817,818 Β· updates every 60s
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