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Block #621,207

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/7/2014, 7:49:40 AM Β· Difficulty 10.9516 Β· 6,193,845 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4060fc279eef599294cea618cd7a968c2872487d0043e0661cedf022c8ee9c20
View on Chainz β†—

Height

#621,207

Difficulty

10.951603

Transactions

1

Size

206 B

Version

2

Bits

0af39c46

Nonce

2,550,572,836

Timestamp

7/7/2014, 7:49:40 AM

Confirmations

6,193,845

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

3c23be2e5f16241c62ae981f6b26df1603b29513348e96a0fa8a50974ee5a229
Transactions (1)
Coinbase3c23be2e5f1624…8a50974ee5a229
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
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.

6.823 Γ— 10⁹⁡(96-digit number)
68237160893212737451…15352790511416363851
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
6.823 Γ— 10⁹⁡(96-digit number)
68237160893212737451…15352790511416363851
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.364 Γ— 10⁹⁢(97-digit number)
13647432178642547490…30705581022832727701
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.729 Γ— 10⁹⁢(97-digit number)
27294864357285094980…61411162045665455401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.458 Γ— 10⁹⁢(97-digit number)
54589728714570189960…22822324091330910801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.091 Γ— 10⁹⁷(98-digit number)
10917945742914037992…45644648182661821601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.183 Γ— 10⁹⁷(98-digit number)
21835891485828075984…91289296365323643201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.367 Γ— 10⁹⁷(98-digit number)
43671782971656151968…82578592730647286401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.734 Γ— 10⁹⁷(98-digit number)
87343565943312303937…65157185461294572801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.746 Γ— 10⁹⁸(99-digit number)
17468713188662460787…30314370922589145601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.493 Γ— 10⁹⁸(99-digit number)
34937426377324921574…60628741845178291201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.987 Γ— 10⁹⁸(99-digit number)
69874852754649843149…21257483690356582401
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:57,764,507 XPMΒ·at block #6,815,051 Β· updates every 60s
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