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Block #63,772

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/19/2013, 3:30:46 AM Β· Difficulty 8.9800 Β· 6,741,785 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d33f67d0f0bd6f05f83ba790364e596f60f4f97bf709f98f21f7fbe1528a8bb5
View on Chainz β†—

Height

#63,772

Difficulty

8.980038

Transactions

2

Size

358 B

Version

2

Bits

08fae3c1

Nonce

502

Timestamp

7/19/2013, 3:30:46 AM

Confirmations

6,741,785

Mined by

⛏️ P2SHAGY4TBx7s42EHEAbrwoVx7JoxEYfD8h7Va

Merkle Root

f448f98346bc1502a52df845ff69d88a1ef4a3fc870bad9b70c478d303efad92
Transactions (2)
Coinbasebd69770fa7de64…288709a34ce3a7
1 in β†’ 1 out12.3900 XPM109 B
AGY4TBx7…YfD8h7Va
6944b8086d4cda…1976f446077bb3
1 in β†’ 1 out12.4200 XPM158 B
AJvx7REd…1ywUzx6z
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.

1.361 Γ— 10⁹⁢(97-digit number)
13616166636613175775…15017719080649659331
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
1.361 Γ— 10⁹⁢(97-digit number)
13616166636613175775…15017719080649659331
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.723 Γ— 10⁹⁢(97-digit number)
27232333273226351551…30035438161299318661
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.446 Γ— 10⁹⁢(97-digit number)
54464666546452703103…60070876322598637321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.089 Γ— 10⁹⁷(98-digit number)
10892933309290540620…20141752645197274641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.178 Γ— 10⁹⁷(98-digit number)
21785866618581081241…40283505290394549281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.357 Γ— 10⁹⁷(98-digit number)
43571733237162162482…80567010580789098561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.714 Γ— 10⁹⁷(98-digit number)
87143466474324324964…61134021161578197121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.742 Γ— 10⁹⁸(99-digit number)
17428693294864864992…22268042323156394241
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,688,535 XPMΒ·at block #6,805,556 Β· updates every 60s
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