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Block #872,430

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/28/2014, 4:56:41 PM Β· Difficulty 10.9635 Β· 5,954,288 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6005b0764824801d4786c76266712e978475e84fd72e6549fa003395bba778fa
View on Chainz β†—

Height

#872,430

Difficulty

10.963546

Transactions

2

Size

879 B

Version

2

Bits

0af6aaf9

Nonce

91,043,010

Timestamp

12/28/2014, 4:56:41 PM

Confirmations

5,954,288

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

50ffc45be0a5e4e4c37c929889c794a40d9a8f56b04c53b894316b6a1918dae3
Transactions (2)
Coinbasedea0c5c90bd8f1…77714fc1b1738c
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
a4e9dc996ae3de…4ce729e2f17197
4 in β†’ 2 out1254.3392 XPM672 B
AGkH55Vp…kSi9QpTDAHBv1qA6…uyQCkZn7
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.

2.932 Γ— 10⁹⁷(98-digit number)
29323839187955532764…59822674808155095041
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
2.932 Γ— 10⁹⁷(98-digit number)
29323839187955532764…59822674808155095041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.864 Γ— 10⁹⁷(98-digit number)
58647678375911065528…19645349616310190081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.172 Γ— 10⁹⁸(99-digit number)
11729535675182213105…39290699232620380161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.345 Γ— 10⁹⁸(99-digit number)
23459071350364426211…78581398465240760321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.691 Γ— 10⁹⁸(99-digit number)
46918142700728852422…57162796930481520641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.383 Γ— 10⁹⁸(99-digit number)
93836285401457704845…14325593860963041281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.876 Γ— 10⁹⁹(100-digit number)
18767257080291540969…28651187721926082561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.753 Γ— 10⁹⁹(100-digit number)
37534514160583081938…57302375443852165121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.506 Γ— 10⁹⁹(100-digit number)
75069028321166163876…14604750887704330241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.501 Γ— 10¹⁰⁰(101-digit number)
15013805664233232775…29209501775408660481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.002 Γ— 10¹⁰⁰(101-digit number)
30027611328466465550…58419003550817320961
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,857,897 XPMΒ·at block #6,826,717 Β· updates every 60s
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