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Block #3,623,155

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/31/2020, 11:39:58 AM Β· Difficulty 10.9090 Β· 3,217,998 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4a2c237f4090401a13e79397faca352a9bc57a75f474c19c9c9f7f35d5f0fa88
View on Chainz β†—

Height

#3,623,155

Difficulty

10.908966

Transactions

2

Size

722 B

Version

2

Bits

0ae8b207

Nonce

328,787,902

Timestamp

3/31/2020, 11:39:58 AM

Confirmations

3,217,998

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

8bc066718f379f21901c7b5738108af93f6f1b45dec4527ca6e5f51e4bd3a9be
Transactions (2)
Coinbase415d988e445ef3…0be62daf7a0cba
1 in β†’ 1 out8.4900 XPM109 B
ASiq2qtK…VMhmk7yL
19acf4e75c0a5d…f14903e0ebf6ad
3 in β†’ 2 out3000.5366 XPM523 B
AX3W6pJy…NwZ88svUAFnhfyw9…AyM5Lz6f
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.

6.380 Γ— 10⁹³(94-digit number)
63800409383853843792…20359157893806964801
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
6.380 Γ— 10⁹³(94-digit number)
63800409383853843792…20359157893806964801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.276 Γ— 10⁹⁴(95-digit number)
12760081876770768758…40718315787613929601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.552 Γ— 10⁹⁴(95-digit number)
25520163753541537517…81436631575227859201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.104 Γ— 10⁹⁴(95-digit number)
51040327507083075034…62873263150455718401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.020 Γ— 10⁹⁡(96-digit number)
10208065501416615006…25746526300911436801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.041 Γ— 10⁹⁡(96-digit number)
20416131002833230013…51493052601822873601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.083 Γ— 10⁹⁡(96-digit number)
40832262005666460027…02986105203645747201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.166 Γ— 10⁹⁡(96-digit number)
81664524011332920054…05972210407291494401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.633 Γ— 10⁹⁢(97-digit number)
16332904802266584010…11944420814582988801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.266 Γ— 10⁹⁢(97-digit number)
32665809604533168021…23888841629165977601
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,973,587 XPMΒ·at block #6,841,152 Β· updates every 60s
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