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Block #2,165,877

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/18/2017, 11:59:34 AM Β· Difficulty 10.8983 Β· 4,660,558 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2513edbfc23cfb03bf5f67dabc971735c80c090daf0a3cf014c08addb066439d
View on Chainz β†—

Height

#2,165,877

Difficulty

10.898306

Transactions

3

Size

4.07 KB

Version

2

Bits

0ae5f761

Nonce

895,618,733

Timestamp

6/18/2017, 11:59:34 AM

Confirmations

4,660,558

Mined by

⛏️ P2SHAVE89dvkGAbFrjAM1BsJbKSehV2zJvhtrZ

Merkle Root

abf1c1af00e6f0fd3d3d5dae3eb5833497c4b4f170d8dc1e14c61f7216d118f2
Transactions (3)
Coinbasea36215717b8212…15e87743836331
1 in β†’ 1 out8.5200 XPM109 B
AVE89dvk…2zJvhtrZ
d7fcc9fced7785…282b080351ef40
25 in β†’ 1 out3788.6391 XPM3.66 KB
AZ7xo3ni…aXTAFhZR
61a097a1ee1aa4…fbef8a421392c1
1 in β†’ 2 out3.3166 XPM225 B
ALcQY6H7…pHv3956SAeYZTP6b…v53Q54vJ
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.

5.271 Γ— 10⁹⁢(97-digit number)
52714334960679572585…83618584819338649599
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
5.271 Γ— 10⁹⁢(97-digit number)
52714334960679572585…83618584819338649599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.271 Γ— 10⁹⁢(97-digit number)
52714334960679572585…83618584819338649601
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
1.054 Γ— 10⁹⁷(98-digit number)
10542866992135914517…67237169638677299199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.054 Γ— 10⁹⁷(98-digit number)
10542866992135914517…67237169638677299201
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
2.108 Γ— 10⁹⁷(98-digit number)
21085733984271829034…34474339277354598399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.108 Γ— 10⁹⁷(98-digit number)
21085733984271829034…34474339277354598401
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
4.217 Γ— 10⁹⁷(98-digit number)
42171467968543658068…68948678554709196799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.217 Γ— 10⁹⁷(98-digit number)
42171467968543658068…68948678554709196801
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
8.434 Γ— 10⁹⁷(98-digit number)
84342935937087316136…37897357109418393599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.434 Γ— 10⁹⁷(98-digit number)
84342935937087316136…37897357109418393601
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
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 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:57,855,617 XPMΒ·at block #6,826,434 Β· updates every 60s
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