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Block #701,072

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/31/2014, 10:03:52 AM Β· Difficulty 10.9591 Β· 6,106,264 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9ea5ab46e47545809a3d699366c8548ad84c5e1076ede0978c8bab5b2f6cc381
View on Chainz β†—

Height

#701,072

Difficulty

10.959076

Transactions

2

Size

989 B

Version

2

Bits

0af585fb

Nonce

375,101,700

Timestamp

8/31/2014, 10:03:52 AM

Confirmations

6,106,264

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

20706ce6a041d3503277194ddd9fcf9a2b396023011952262764cf8160e984bd
Transactions (2)
Coinbase3f69fe59ad2340…1d2af44d32ec39
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
b0aefcc222cdd9…d5fb4bebfdc56a
5 in β†’ 1 out15.4677 XPM782 B
ATMYSSTw…dhjN1tjK
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.

1.127 Γ— 10⁹⁢(97-digit number)
11279076224957998043…43081905221280499201
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
1.127 Γ— 10⁹⁢(97-digit number)
11279076224957998043…43081905221280499201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.255 Γ— 10⁹⁢(97-digit number)
22558152449915996087…86163810442560998401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.511 Γ— 10⁹⁢(97-digit number)
45116304899831992175…72327620885121996801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.023 Γ— 10⁹⁢(97-digit number)
90232609799663984351…44655241770243993601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.804 Γ— 10⁹⁷(98-digit number)
18046521959932796870…89310483540487987201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.609 Γ— 10⁹⁷(98-digit number)
36093043919865593740…78620967080975974401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.218 Γ— 10⁹⁷(98-digit number)
72186087839731187480…57241934161951948801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.443 Γ— 10⁹⁸(99-digit number)
14437217567946237496…14483868323903897601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.887 Γ— 10⁹⁸(99-digit number)
28874435135892474992…28967736647807795201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.774 Γ— 10⁹⁸(99-digit number)
57748870271784949984…57935473295615590401
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:57,702,706 XPMΒ·at block #6,807,335 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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