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Block #445,711

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/16/2014, 2:13:30 AM Β· Difficulty 10.3566 Β· 6,364,094 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
37f8537ad18f3695b70475c7e7eb1d1c21bc82e9dbdf13ddd87f39bce6c1fb1d
View on Chainz β†—

Height

#445,711

Difficulty

10.356558

Transactions

1

Size

201 B

Version

2

Bits

0a5b475b

Nonce

737,813

Timestamp

3/16/2014, 2:13:30 AM

Confirmations

6,364,094

Mined by

⛏️ P2SHAcFkTYRy41MQMnEgczczmNHzSHmn4VdtDR

Merkle Root

1d13cf14d0857401b803ec0018664f2b0f9b421a8a45d4f75cf7e0a030b95d0e
Transactions (1)
Coinbase1d13cf14d08574…f7e0a030b95d0e
1 in β†’ 1 out9.3100 XPM109 B
AcFkTYRy…mn4VdtDR
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.

2.810 Γ— 10⁹⁸(99-digit number)
28101526071729735304…50381137696118193281
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
2.810 Γ— 10⁹⁸(99-digit number)
28101526071729735304…50381137696118193281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.620 Γ— 10⁹⁸(99-digit number)
56203052143459470609…00762275392236386561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.124 Γ— 10⁹⁹(100-digit number)
11240610428691894121…01524550784472773121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.248 Γ— 10⁹⁹(100-digit number)
22481220857383788243…03049101568945546241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.496 Γ— 10⁹⁹(100-digit number)
44962441714767576487…06098203137891092481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.992 Γ— 10⁹⁹(100-digit number)
89924883429535152974…12196406275782184961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.798 Γ— 10¹⁰⁰(101-digit number)
17984976685907030594…24392812551564369921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.596 Γ— 10¹⁰⁰(101-digit number)
35969953371814061189…48785625103128739841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.193 Γ— 10¹⁰⁰(101-digit number)
71939906743628122379…97571250206257479681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.438 Γ— 10¹⁰¹(102-digit number)
14387981348725624475…95142500412514959361
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:57,722,522 XPMΒ·at block #6,809,804 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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