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Block #1,066,154

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/19/2015, 9:19:42 AM Β· Difficulty 10.7364 Β· 5,734,812 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dde4f6d4bb05d3dcfbb31663f5a67238cbef333ca0a1ac7b0609025007c7d153
View on Chainz β†—

Height

#1,066,154

Difficulty

10.736392

Transactions

2

Size

77.46 KB

Version

2

Bits

0abc842c

Nonce

146,189,075

Timestamp

5/19/2015, 9:19:42 AM

Confirmations

5,734,812

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

1414e3a7a71357b6b88d3c869bded5fff589a92e9efbd14c56afe5a3d1abea46
Transactions (2)
Coinbasea0682d9254ee3f…4bb7c0d65c1cbb
1 in β†’ 1 out9.4600 XPM116 B
ANSXnLY2…Sd25TjkD
7fd0630deb33b6…dcba81309a171a
534 in β†’ 2 out18930.7694 XPM77.26 KB
AKEpP5D3…7dd4dF7JAc7TmQJ3…F6w332Yr
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.

6.623 Γ— 10⁹⁢(97-digit number)
66239765623344463821…08264421507649495041
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
6.623 Γ— 10⁹⁢(97-digit number)
66239765623344463821…08264421507649495041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.324 Γ— 10⁹⁷(98-digit number)
13247953124668892764…16528843015298990081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.649 Γ— 10⁹⁷(98-digit number)
26495906249337785528…33057686030597980161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.299 Γ— 10⁹⁷(98-digit number)
52991812498675571057…66115372061195960321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.059 Γ— 10⁹⁸(99-digit number)
10598362499735114211…32230744122391920641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.119 Γ— 10⁹⁸(99-digit number)
21196724999470228422…64461488244783841281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.239 Γ— 10⁹⁸(99-digit number)
42393449998940456845…28922976489567682561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.478 Γ— 10⁹⁸(99-digit number)
84786899997880913691…57845952979135365121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.695 Γ— 10⁹⁹(100-digit number)
16957379999576182738…15691905958270730241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.391 Γ— 10⁹⁹(100-digit number)
33914759999152365476…31383811916541460481
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:57,651,786 XPMΒ·at block #6,800,965 Β· updates every 60s
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