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Block #2,703,207

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/13/2018, 4:49:54 AM Β· Difficulty 11.6287 Β· 4,139,745 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
af20b560b2453a9c18bdd3c21be167115d9d1c73d7b9b1e34de860c6b2ffd0d1
View on Chainz β†—

Height

#2,703,207

Difficulty

11.628659

Transactions

1

Size

199 B

Version

2

Bits

0ba0efcb

Nonce

38,688,531

Timestamp

6/13/2018, 4:49:54 AM

Confirmations

4,139,745

Mined by

⛏️ P2SHAPUDgAU6sVTsDNAJJA2Dp5wv2V6pFQJDvh

Merkle Root

77c22dc502e902b7f4a75c486dcbc2c5c4b507d194642dc9737b452a154449d6
Transactions (1)
Coinbase77c22dc502e902…7b452a154449d6
1 in β†’ 1 out7.3800 XPM109 B
APUDgAU6…6pFQJDvh
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.

5.600 Γ— 10⁹⁴(95-digit number)
56003191725924044448…26699242575327000161
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
5.600 Γ— 10⁹⁴(95-digit number)
56003191725924044448…26699242575327000161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.120 Γ— 10⁹⁡(96-digit number)
11200638345184808889…53398485150654000321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.240 Γ— 10⁹⁡(96-digit number)
22401276690369617779…06796970301308000641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.480 Γ— 10⁹⁡(96-digit number)
44802553380739235558…13593940602616001281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.960 Γ— 10⁹⁡(96-digit number)
89605106761478471117…27187881205232002561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.792 Γ— 10⁹⁢(97-digit number)
17921021352295694223…54375762410464005121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.584 Γ— 10⁹⁢(97-digit number)
35842042704591388447…08751524820928010241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.168 Γ— 10⁹⁢(97-digit number)
71684085409182776894…17503049641856020481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.433 Γ— 10⁹⁷(98-digit number)
14336817081836555378…35006099283712040961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.867 Γ— 10⁹⁷(98-digit number)
28673634163673110757…70012198567424081921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.734 Γ— 10⁹⁷(98-digit number)
57347268327346221515…40024397134848163841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
1.146 Γ— 10⁹⁸(99-digit number)
11469453665469244303…80048794269696327681
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,987,968 XPMΒ·at block #6,842,951 Β· updates every 60s
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