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Block #2,256,889

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/18/2017, 6:38:12 AM Β· Difficulty 10.9516 Β· 4,575,984 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
fbde6b52bf7ae80ac4ac33c25532deedcee348c95ff59674af6fdc8ded056d37
View on Chainz β†—

Height

#2,256,889

Difficulty

10.951572

Transactions

2

Size

51.54 KB

Version

2

Bits

0af39a3c

Nonce

1,141,260,736

Timestamp

8/18/2017, 6:38:12 AM

Confirmations

4,575,984

Mined by

⛏️ P2SHAewKNpA3x26szEASJT3bycmFiKPVZ3EG38

Merkle Root

341d189c6517bb7f28d2ae70d86f89857343522d0a503e38c5c01dc1ff555c19
Transactions (2)
Coinbasec12ff51e095ffd…93ebdde26ec28b
1 in β†’ 1 out8.8500 XPM109 B
AewKNpA3…PVZ3EG38
622f64044051d8…0581251e20bdce
355 in β†’ 1 out37487.7525 XPM51.34 KB
APXfqgS8…taxNGKAY
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.

1.937 Γ— 10⁹³(94-digit number)
19372339556814388724…25735540437002469441
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
1.937 Γ— 10⁹³(94-digit number)
19372339556814388724…25735540437002469441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.874 Γ— 10⁹³(94-digit number)
38744679113628777448…51471080874004938881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.748 Γ— 10⁹³(94-digit number)
77489358227257554896…02942161748009877761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.549 Γ— 10⁹⁴(95-digit number)
15497871645451510979…05884323496019755521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.099 Γ— 10⁹⁴(95-digit number)
30995743290903021958…11768646992039511041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.199 Γ— 10⁹⁴(95-digit number)
61991486581806043917…23537293984079022081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.239 Γ— 10⁹⁡(96-digit number)
12398297316361208783…47074587968158044161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.479 Γ— 10⁹⁡(96-digit number)
24796594632722417566…94149175936316088321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.959 Γ— 10⁹⁡(96-digit number)
49593189265444835133…88298351872632176641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.918 Γ— 10⁹⁡(96-digit number)
99186378530889670267…76596703745264353281
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:57,907,152 XPMΒ·at block #6,832,872 Β· updates every 60s
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