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Block #709,612

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/6/2014, 1:28:42 PM Β· Difficulty 10.9568 Β· 6,101,491 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
798db5ed9c826e6f66d6d52880e50a4e89ee0fe74bc0d0a81758d4ad268eff05
View on Chainz β†—

Height

#709,612

Difficulty

10.956804

Transactions

4

Size

6.04 KB

Version

2

Bits

0af4f11f

Nonce

723,314,545

Timestamp

9/6/2014, 1:28:42 PM

Confirmations

6,101,491

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

352c94c591047392c15ffc3d226c651f4f3a97cd1069151e4831c20770141db8
Transactions (4)
Coinbased1cb7e6755d3c1…ed412275d4a574
1 in β†’ 1 out8.4075 XPM116 B
ANSXnLY2…Sd25TjkD
48626a716ae768…1a428d2a5bfb57
35 in β†’ 1 out1423.0200 XPM5.10 KB
AVKgP6f1…JS18wmDq
bb35bee34bad6f…9f495bce9e384e
2 in β†’ 2 out10.1607 XPM373 B
AbcdY8zJ…V4YUzF9vAYay2Lg1…b7UcHZjF
56fe517a26ef85…e396ecea13fc1a
2 in β†’ 2 out6.1733 XPM374 B
AGAht2CN…6pHKm9M5AQYwMk1X…LPHb2iJb
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.

4.496 Γ— 10⁹⁢(97-digit number)
44967498850188128495…94101461615692450401
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
4.496 Γ— 10⁹⁢(97-digit number)
44967498850188128495…94101461615692450401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.993 Γ— 10⁹⁢(97-digit number)
89934997700376256990…88202923231384900801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.798 Γ— 10⁹⁷(98-digit number)
17986999540075251398…76405846462769801601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.597 Γ— 10⁹⁷(98-digit number)
35973999080150502796…52811692925539603201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.194 Γ— 10⁹⁷(98-digit number)
71947998160301005592…05623385851079206401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.438 Γ— 10⁹⁸(99-digit number)
14389599632060201118…11246771702158412801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.877 Γ— 10⁹⁸(99-digit number)
28779199264120402236…22493543404316825601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.755 Γ— 10⁹⁸(99-digit number)
57558398528240804473…44987086808633651201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.151 Γ— 10⁹⁹(100-digit number)
11511679705648160894…89974173617267302401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.302 Γ— 10⁹⁹(100-digit number)
23023359411296321789…79948347234534604801
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:57,732,931 XPMΒ·at block #6,811,102 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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