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Block #2,128,655

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/23/2017, 12:50:58 AM Β· Difficulty 10.9137 Β· 4,713,132 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e6ce05b6eaa1f5be8259ac953650b1a3f394ce5e1a4ee87bf7c6229e65b0ef56
View on Chainz β†—

Height

#2,128,655

Difficulty

10.913689

Transactions

1

Size

242 B

Version

2

Bits

0ae9e784

Nonce

2,179,273,274

Timestamp

5/23/2017, 12:50:58 AM

Confirmations

4,713,132

Mined by

⛏️ P2SHAMMJ7Ku9ctFmjCbBPtKsnh34K5ZYGbYo5z

Merkle Root

8bc7451201b20bdb0d77ca00479346d90a10e40a55f16bc4c379b8bd4c6f84b9
Transactions (1)
Coinbase8bc7451201b20b…79b8bd4c6f84b9
1 in β†’ 2 out8.3800 XPM152 B
AMMJ7Ku9…ZYGbYo5zAXbk7f7A…Tx7JECPG
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.

2.976 Γ— 10⁹⁡(96-digit number)
29768147406271182556…77279554933645143661
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
2.976 Γ— 10⁹⁡(96-digit number)
29768147406271182556…77279554933645143661
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.953 Γ— 10⁹⁡(96-digit number)
59536294812542365113…54559109867290287321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.190 Γ— 10⁹⁢(97-digit number)
11907258962508473022…09118219734580574641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.381 Γ— 10⁹⁢(97-digit number)
23814517925016946045…18236439469161149281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.762 Γ— 10⁹⁢(97-digit number)
47629035850033892090…36472878938322298561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.525 Γ— 10⁹⁢(97-digit number)
95258071700067784181…72945757876644597121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.905 Γ— 10⁹⁷(98-digit number)
19051614340013556836…45891515753289194241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.810 Γ— 10⁹⁷(98-digit number)
38103228680027113672…91783031506578388481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.620 Γ— 10⁹⁷(98-digit number)
76206457360054227345…83566063013156776961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.524 Γ— 10⁹⁸(99-digit number)
15241291472010845469…67132126026313553921
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:57,978,674 XPMΒ·at block #6,841,786 Β· updates every 60s
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