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Block #2,855,608

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/26/2018, 8:49:24 AM Β· Difficulty 11.6980 Β· 3,986,749 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7a65986b0a7bffecaa154201e73e6efef6232b4429d4677ddde9c8c121708116
View on Chainz β†—

Height

#2,855,608

Difficulty

11.698044

Transactions

1

Size

201 B

Version

2

Bits

0bb2b309

Nonce

2,085,878,418

Timestamp

9/26/2018, 8:49:24 AM

Confirmations

3,986,749

Mined by

⛏️ P2SHAbu7seEyTUkfyR1Vgxx7mEv9njgZnADLGL

Merkle Root

ada53f4d301bfe4742d3a7be0a9c0e67652143a000630df9bf444c40cad40265
Transactions (1)
Coinbaseada53f4d301bfe…444c40cad40265
1 in β†’ 1 out7.3000 XPM110 B
Abu7seEy…gZnADLGL
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.

8.507 Γ— 10⁹⁢(97-digit number)
85077316971636102617…84170767475531653119
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
8.507 Γ— 10⁹⁢(97-digit number)
85077316971636102617…84170767475531653119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.507 Γ— 10⁹⁢(97-digit number)
85077316971636102617…84170767475531653121
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
1.701 Γ— 10⁹⁷(98-digit number)
17015463394327220523…68341534951063306239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.701 Γ— 10⁹⁷(98-digit number)
17015463394327220523…68341534951063306241
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
3.403 Γ— 10⁹⁷(98-digit number)
34030926788654441046…36683069902126612479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.403 Γ— 10⁹⁷(98-digit number)
34030926788654441046…36683069902126612481
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
6.806 Γ— 10⁹⁷(98-digit number)
68061853577308882093…73366139804253224959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.806 Γ— 10⁹⁷(98-digit number)
68061853577308882093…73366139804253224961
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
1.361 Γ— 10⁹⁸(99-digit number)
13612370715461776418…46732279608506449919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.361 Γ— 10⁹⁸(99-digit number)
13612370715461776418…46732279608506449921
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
2.722 Γ— 10⁹⁸(99-digit number)
27224741430923552837…93464559217012899839
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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