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Block #666,937

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/7/2014, 9:00:31 AM Β· Difficulty 10.9618 Β· 6,160,070 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7c82d609125dbde0f6dee65594a538f6e0215cf32ba43726e1409587b73c7ce4
View on Chainz β†—

Height

#666,937

Difficulty

10.961808

Transactions

2

Size

581 B

Version

2

Bits

0af63906

Nonce

1,491,910,476

Timestamp

8/7/2014, 9:00:31 AM

Confirmations

6,160,070

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

831d3419e777661a1b5b3725af5e84e4a6eeae1c8693f9b7d499d4987327a6c3
Transactions (2)
Coinbase0064e640e983f5…da25147a5507ef
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
4575a2330b3e58…b19ced1d7b9520
2 in β†’ 2 out6.5381 XPM375 B
AHcSEkJ5…pb4fDYmkAW6xKVVP…sFp5odmT
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.

2.193 Γ— 10⁹⁡(96-digit number)
21937143725844321619…71261561267773932801
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
2.193 Γ— 10⁹⁡(96-digit number)
21937143725844321619…71261561267773932801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.387 Γ— 10⁹⁡(96-digit number)
43874287451688643239…42523122535547865601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.774 Γ— 10⁹⁡(96-digit number)
87748574903377286479…85046245071095731201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.754 Γ— 10⁹⁢(97-digit number)
17549714980675457295…70092490142191462401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.509 Γ— 10⁹⁢(97-digit number)
35099429961350914591…40184980284382924801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.019 Γ— 10⁹⁢(97-digit number)
70198859922701829183…80369960568765849601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.403 Γ— 10⁹⁷(98-digit number)
14039771984540365836…60739921137531699201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.807 Γ— 10⁹⁷(98-digit number)
28079543969080731673…21479842275063398401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.615 Γ— 10⁹⁷(98-digit number)
56159087938161463346…42959684550126796801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.123 Γ— 10⁹⁸(99-digit number)
11231817587632292669…85919369100253593601
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:57,860,232 XPMΒ·at block #6,827,006 Β· updates every 60s
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