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Block #2,168,754

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/20/2017, 11:49:34 AM Β· Difficulty 10.8985 Β· 4,657,894 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9731422d896b8cac37a20960cf34dbae30d90e70e9362012c575bf0bcedd02a5
View on Chainz β†—

Height

#2,168,754

Difficulty

10.898502

Transactions

2

Size

4.03 KB

Version

2

Bits

0ae6043c

Nonce

1,060,645,906

Timestamp

6/20/2017, 11:49:34 AM

Confirmations

4,657,894

Mined by

⛏️ P2SHARYCWe8WcHtkhKKVBAqxEmTvoca9TCgcmb

Merkle Root

9c4d79568a5f643f39633247bcf602f4b0f747d379b68c9a6e0083d41a7b006b
Transactions (2)
Coinbase239ff0b3b5c2d0…9eecf88f073650
1 in β†’ 1 out8.4900 XPM109 B
ARYCWe8W…a9TCgcmb
1bf352752fc14a…1c13f2f7820d2f
26 in β†’ 2 out226.2347 XPM3.83 KB
AdGePube…izaEfFL4AR1nxGbG…up7VnJmw
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.

6.452 Γ— 10⁹⁴(95-digit number)
64525797737296470218…33506617519708001599
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
6.452 Γ— 10⁹⁴(95-digit number)
64525797737296470218…33506617519708001599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.452 Γ— 10⁹⁴(95-digit number)
64525797737296470218…33506617519708001601
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
1.290 Γ— 10⁹⁡(96-digit number)
12905159547459294043…67013235039416003199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.290 Γ— 10⁹⁡(96-digit number)
12905159547459294043…67013235039416003201
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
2.581 Γ— 10⁹⁡(96-digit number)
25810319094918588087…34026470078832006399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.581 Γ— 10⁹⁡(96-digit number)
25810319094918588087…34026470078832006401
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
5.162 Γ— 10⁹⁡(96-digit number)
51620638189837176175…68052940157664012799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.162 Γ— 10⁹⁡(96-digit number)
51620638189837176175…68052940157664012801
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
1.032 Γ— 10⁹⁢(97-digit number)
10324127637967435235…36105880315328025599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.032 Γ— 10⁹⁢(97-digit number)
10324127637967435235…36105880315328025601
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
2.064 Γ— 10⁹⁢(97-digit number)
20648255275934870470…72211760630656051199
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:57,857,332 XPMΒ·at block #6,826,647 Β· updates every 60s
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