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Block #3,009,562

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/14/2019, 5:30:05 PM Β· Difficulty 11.2007 Β· 3,823,711 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1bcebc738580675a8594e8cea3978afc4c8e6fd2e63b0c12e74d8406c437d980
View on Chainz β†—

Height

#3,009,562

Difficulty

11.200677

Transactions

2

Size

541 B

Version

2

Bits

0b335f92

Nonce

1,535,223,119

Timestamp

1/14/2019, 5:30:05 PM

Confirmations

3,823,711

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

6c4e36d1105d66ccd54a462fea8831d1ae1105587b16207ede2763f34289a69c
Transactions (2)
Coinbase7bea3627439704…f893f16e89fa20
1 in β†’ 1 out7.9700 XPM110 B
AbXwmGxD…4XXYP765
fec8ae23cc571e…c6361f3f055d2b
2 in β†’ 2 out11.9166 XPM340 B
AbXwmGxD…4XXYP765AMfZL8Sg…3KgjLnV7
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.

2.191 Γ— 10⁹⁷(98-digit number)
21914884109345821777…57141645400030699521
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
2.191 Γ— 10⁹⁷(98-digit number)
21914884109345821777…57141645400030699521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.382 Γ— 10⁹⁷(98-digit number)
43829768218691643554…14283290800061399041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.765 Γ— 10⁹⁷(98-digit number)
87659536437383287109…28566581600122798081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.753 Γ— 10⁹⁸(99-digit number)
17531907287476657421…57133163200245596161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.506 Γ— 10⁹⁸(99-digit number)
35063814574953314843…14266326400491192321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.012 Γ— 10⁹⁸(99-digit number)
70127629149906629687…28532652800982384641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.402 Γ— 10⁹⁹(100-digit number)
14025525829981325937…57065305601964769281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.805 Γ— 10⁹⁹(100-digit number)
28051051659962651875…14130611203929538561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.610 Γ— 10⁹⁹(100-digit number)
56102103319925303750…28261222407859077121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.122 Γ— 10¹⁰⁰(101-digit number)
11220420663985060750…56522444815718154241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.244 Γ— 10¹⁰⁰(101-digit number)
22440841327970121500…13044889631436308481
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:57,910,378 XPMΒ·at block #6,833,272 Β· updates every 60s
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