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Block #3,050,707

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/13/2019, 5:45:09 AM Β· Difficulty 10.9961 Β· 3,791,285 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0aba32090e68c3ee529dddb02f27a34d265b7f7c286f895feba2ff7f868cd7bc
View on Chainz β†—

Height

#3,050,707

Difficulty

10.996061

Transactions

1

Size

199 B

Version

2

Bits

0afefddb

Nonce

1,535,166,617

Timestamp

2/13/2019, 5:45:09 AM

Confirmations

3,791,285

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

65abdfad76415aa578e35784c23a7af97a91db13ea4324754e329eea5ff8a786
Transactions (1)
Coinbase65abdfad76415a…329eea5ff8a786
1 in β†’ 1 out8.2600 XPM109 B
AUhjokok…k5m93PZR
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.

4.378 Γ— 10⁹⁴(95-digit number)
43782256892143831973…18829211893994907321
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
4.378 Γ— 10⁹⁴(95-digit number)
43782256892143831973…18829211893994907321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.756 Γ— 10⁹⁴(95-digit number)
87564513784287663946…37658423787989814641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.751 Γ— 10⁹⁡(96-digit number)
17512902756857532789…75316847575979629281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.502 Γ— 10⁹⁡(96-digit number)
35025805513715065578…50633695151959258561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.005 Γ— 10⁹⁡(96-digit number)
70051611027430131157…01267390303918517121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.401 Γ— 10⁹⁢(97-digit number)
14010322205486026231…02534780607837034241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.802 Γ— 10⁹⁢(97-digit number)
28020644410972052462…05069561215674068481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.604 Γ— 10⁹⁢(97-digit number)
56041288821944104925…10139122431348136961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.120 Γ— 10⁹⁷(98-digit number)
11208257764388820985…20278244862696273921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.241 Γ— 10⁹⁷(98-digit number)
22416515528777641970…40556489725392547841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.483 Γ— 10⁹⁷(98-digit number)
44833031057555283940…81112979450785095681
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:57,980,323 XPMΒ·at block #6,841,991 Β· updates every 60s
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