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Block #3,412,473

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/30/2019, 6:51:30 AM Β· Difficulty 10.9850 Β· 3,428,313 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e029a12d85ba7257bc84c38f80ea1fffc720892cc6ae1849f07b6cdf887a7130
View on Chainz β†—

Height

#3,412,473

Difficulty

10.984958

Transactions

1

Size

200 B

Version

2

Bits

0afc2639

Nonce

1,813,866,492

Timestamp

10/30/2019, 6:51:30 AM

Confirmations

3,428,313

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

80d86dd03f119029fd29fd22e76b8da59b2c8d41ff40369ac2a42cbf7f0545b6
Transactions (1)
Coinbase80d86dd03f1190…a42cbf7f0545b6
1 in β†’ 1 out8.2700 XPM109 B
ASiq2qtK…VMhmk7yL
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.

1.218 Γ— 10⁹⁢(97-digit number)
12187674268628577760…98854311430333209601
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
1.218 Γ— 10⁹⁢(97-digit number)
12187674268628577760…98854311430333209601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.437 Γ— 10⁹⁢(97-digit number)
24375348537257155521…97708622860666419201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.875 Γ— 10⁹⁢(97-digit number)
48750697074514311042…95417245721332838401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.750 Γ— 10⁹⁢(97-digit number)
97501394149028622085…90834491442665676801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.950 Γ— 10⁹⁷(98-digit number)
19500278829805724417…81668982885331353601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.900 Γ— 10⁹⁷(98-digit number)
39000557659611448834…63337965770662707201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.800 Γ— 10⁹⁷(98-digit number)
78001115319222897668…26675931541325414401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.560 Γ— 10⁹⁸(99-digit number)
15600223063844579533…53351863082650828801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.120 Γ— 10⁹⁸(99-digit number)
31200446127689159067…06703726165301657601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.240 Γ— 10⁹⁸(99-digit number)
62400892255378318134…13407452330603315201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.248 Γ— 10⁹⁹(100-digit number)
12480178451075663626…26814904661206630401
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:57,970,634 XPMΒ·at block #6,840,785 Β· updates every 60s
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