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Block #2,540,870

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 2/27/2018, 12:28:08 PM Β· Difficulty 10.9871 Β· 4,295,592 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5f8c48ff0461daf8e2f0fb0cb9613888f0d2e27a8b238dd822d47d7bee5ae1c5
View on Chainz β†—

Height

#2,540,870

Difficulty

10.987124

Transactions

2

Size

424 B

Version

2

Bits

0afcb421

Nonce

296,751,664

Timestamp

2/27/2018, 12:28:08 PM

Confirmations

4,295,592

Mined by

⛏️ P2SHAQJGw3DPdJmYRdGWttSzTuEawxv63PfsHd

Merkle Root

ce09f5579bb8e178563a4e3e1508e8b6a92606810374db750b70652670d5e170
Transactions (2)
Coinbase1599e86aca24c7…0ab2a5f82ca569
1 in β†’ 1 out8.2800 XPM109 B
AQJGw3DP…v63PfsHd
f7570d938e539d…10dcb53b4e7e95
1 in β†’ 2 out7.9900 XPM225 B
ALe9QnJq…RNrbKD3hAKc39hVX…7bmt7o94
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.

7.629 Γ— 10⁹⁴(95-digit number)
76296991829974938789…72226359303488507359
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
7.629 Γ— 10⁹⁴(95-digit number)
76296991829974938789…72226359303488507359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.629 Γ— 10⁹⁴(95-digit number)
76296991829974938789…72226359303488507361
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
1.525 Γ— 10⁹⁡(96-digit number)
15259398365994987757…44452718606977014719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.525 Γ— 10⁹⁡(96-digit number)
15259398365994987757…44452718606977014721
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
3.051 Γ— 10⁹⁡(96-digit number)
30518796731989975515…88905437213954029439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.051 Γ— 10⁹⁡(96-digit number)
30518796731989975515…88905437213954029441
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
6.103 Γ— 10⁹⁡(96-digit number)
61037593463979951031…77810874427908058879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.103 Γ— 10⁹⁡(96-digit number)
61037593463979951031…77810874427908058881
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
1.220 Γ— 10⁹⁢(97-digit number)
12207518692795990206…55621748855816117759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.220 Γ— 10⁹⁢(97-digit number)
12207518692795990206…55621748855816117761
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
2.441 Γ— 10⁹⁢(97-digit number)
24415037385591980412…11243497711632235519
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:57,935,968 XPMΒ·at block #6,836,461 Β· updates every 60s
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