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Block #2,831,280

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/9/2018, 5:34:49 AM Β· Difficulty 11.7172 Β· 4,011,077 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5a8c401d92d2d5845e329a4c556b1aee011a89a3fcdda75ca54cf586f51822c7
View on Chainz β†—

Height

#2,831,280

Difficulty

11.717240

Transactions

1

Size

200 B

Version

2

Bits

0bb79d0c

Nonce

1,955,734,580

Timestamp

9/9/2018, 5:34:49 AM

Confirmations

4,011,077

Mined by

⛏️ P2SHAKP1m2KkY1w6D7VvioiciBqqtS4zq8kytM

Merkle Root

c85378fe43473e84298036eb619db279c6ac9e07f29609a0283162120ae7b211
Transactions (1)
Coinbasec85378fe43473e…3162120ae7b211
1 in β†’ 1 out7.2700 XPM110 B
AKP1m2Kk…4zq8kytM
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.

5.378 Γ— 10⁹³(94-digit number)
53787558255994694261…59450443518826550039
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
5.378 Γ— 10⁹³(94-digit number)
53787558255994694261…59450443518826550039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.378 Γ— 10⁹³(94-digit number)
53787558255994694261…59450443518826550041
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
1.075 Γ— 10⁹⁴(95-digit number)
10757511651198938852…18900887037653100079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.075 Γ— 10⁹⁴(95-digit number)
10757511651198938852…18900887037653100081
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
2.151 Γ— 10⁹⁴(95-digit number)
21515023302397877704…37801774075306200159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.151 Γ— 10⁹⁴(95-digit number)
21515023302397877704…37801774075306200161
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
4.303 Γ— 10⁹⁴(95-digit number)
43030046604795755409…75603548150612400319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.303 Γ— 10⁹⁴(95-digit number)
43030046604795755409…75603548150612400321
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
8.606 Γ— 10⁹⁴(95-digit number)
86060093209591510818…51207096301224800639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.606 Γ— 10⁹⁴(95-digit number)
86060093209591510818…51207096301224800641
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
1.721 Γ— 10⁹⁡(96-digit number)
17212018641918302163…02414192602449601279
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
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