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Block #1,542,922

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/15/2016, 7:37:12 PM Β· Difficulty 10.6514 Β· 5,271,176 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dfa3de4e7d957cd93b69feece682a09cea6a1357de4ef0935893cdf0eb30e5a1
View on Chainz β†—

Height

#1,542,922

Difficulty

10.651403

Transactions

1

Size

199 B

Version

2

Bits

0aa6c257

Nonce

72,028

Timestamp

4/15/2016, 7:37:12 PM

Confirmations

5,271,176

Mined by

⛏️ P2SHAVUSTGLfXSGYjUDuVVpW48qmaeSeYSsAGR

Merkle Root

a766c5158663cb25526a9750b0b93dbe5e6815d0a1aa18b1ea7c9ec5c5c801ba
Transactions (1)
Coinbasea766c5158663cb…7c9ec5c5c801ba
1 in β†’ 1 out8.8000 XPM109 B
AVUSTGLf…SeYSsAGR
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.

7.571 Γ— 10⁹⁡(96-digit number)
75713943237651923460…07536857851580530321
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
7.571 Γ— 10⁹⁡(96-digit number)
75713943237651923460…07536857851580530321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.514 Γ— 10⁹⁢(97-digit number)
15142788647530384692…15073715703161060641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.028 Γ— 10⁹⁢(97-digit number)
30285577295060769384…30147431406322121281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.057 Γ— 10⁹⁢(97-digit number)
60571154590121538768…60294862812644242561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.211 Γ— 10⁹⁷(98-digit number)
12114230918024307753…20589725625288485121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.422 Γ— 10⁹⁷(98-digit number)
24228461836048615507…41179451250576970241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.845 Γ— 10⁹⁷(98-digit number)
48456923672097231014…82358902501153940481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.691 Γ— 10⁹⁷(98-digit number)
96913847344194462029…64717805002307880961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.938 Γ— 10⁹⁸(99-digit number)
19382769468838892405…29435610004615761921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.876 Γ— 10⁹⁸(99-digit number)
38765538937677784811…58871220009231523841
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:57,756,866 XPMΒ·at block #6,814,097 Β· updates every 60s
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