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Block #2,810,770

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/26/2018, 1:29:21 PM Β· Difficulty 11.6663 Β· 4,034,555 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
882bbda6b085244d21dc076c9ac345155c58407c0ae9c4220d2b6371a39e4835
View on Chainz β†—

Height

#2,810,770

Difficulty

11.666314

Transactions

1

Size

201 B

Version

2

Bits

0baa9396

Nonce

90,998,011

Timestamp

8/26/2018, 1:29:21 PM

Confirmations

4,034,555

Mined by

⛏️ P2SHAWnR4m5WsifbUvozaYN5YmeUsewzWDUk2w

Merkle Root

9907ad9065dc790922b9e7d94b6f73d472a92488528805d230ff2d636912aad0
Transactions (1)
Coinbase9907ad9065dc79…ff2d636912aad0
1 in β†’ 1 out7.3400 XPM110 B
AWnR4m5W…wzWDUk2w
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.

7.755 Γ— 10⁹⁷(98-digit number)
77553444629566118361…49912783015779287039
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 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.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
7.755 Γ— 10⁹⁷(98-digit number)
77553444629566118361…49912783015779287039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.755 Γ— 10⁹⁷(98-digit number)
77553444629566118361…49912783015779287041
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.551 Γ— 10⁹⁸(99-digit number)
15510688925913223672…99825566031558574079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.551 Γ— 10⁹⁸(99-digit number)
15510688925913223672…99825566031558574081
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
3.102 Γ— 10⁹⁸(99-digit number)
31021377851826447344…99651132063117148159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.102 Γ— 10⁹⁸(99-digit number)
31021377851826447344…99651132063117148161
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
6.204 Γ— 10⁹⁸(99-digit number)
62042755703652894689…99302264126234296319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.204 Γ— 10⁹⁸(99-digit number)
62042755703652894689…99302264126234296321
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
1.240 Γ— 10⁹⁹(100-digit number)
12408551140730578937…98604528252468592639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.240 Γ— 10⁹⁹(100-digit number)
12408551140730578937…98604528252468592641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
2.481 Γ— 10⁹⁹(100-digit number)
24817102281461157875…97209056504937185279
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 Bi-Twin Chain. 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 TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:58,007,040 XPMΒ·at block #6,845,324 Β· updates every 60s
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