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Block #2,866,685

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/4/2018, 9:32:15 AM Β· Difficulty 11.6680 Β· 3,973,999 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
27041597f612a9e935d27a0c72b83f31897b70a27b0b40072a312938450e1a4e
View on Chainz β†—

Height

#2,866,685

Difficulty

11.668037

Transactions

2

Size

540 B

Version

2

Bits

0bab0479

Nonce

524,588,837

Timestamp

10/4/2018, 9:32:15 AM

Confirmations

3,973,999

Mined by

⛏️ P2SHANP1NUKHGJAUZ4uoX7Ty3oBnBZv4JLVh4h

Merkle Root

b4bf337f378bb75539ace83249394308fb8fa3edcfdcd37ef01cb87bdac17d67
Transactions (2)
Coinbase084755dfb442f0…a5e1f66d9a7652
1 in β†’ 1 out7.3400 XPM109 B
ANP1NUKH…v4JLVh4h
00cddf99e0f9f8…e39420f25574a9
2 in β†’ 2 out11.9500 XPM341 B
AXVX3yMb…y41LWnYzAek7aQzY…4495YRvK
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.

2.131 Γ— 10⁹⁴(95-digit number)
21314693955347566197…97479916070370114399
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
2.131 Γ— 10⁹⁴(95-digit number)
21314693955347566197…97479916070370114399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.131 Γ— 10⁹⁴(95-digit number)
21314693955347566197…97479916070370114401
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
4.262 Γ— 10⁹⁴(95-digit number)
42629387910695132394…94959832140740228799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.262 Γ— 10⁹⁴(95-digit number)
42629387910695132394…94959832140740228801
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
8.525 Γ— 10⁹⁴(95-digit number)
85258775821390264789…89919664281480457599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.525 Γ— 10⁹⁴(95-digit number)
85258775821390264789…89919664281480457601
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
1.705 Γ— 10⁹⁡(96-digit number)
17051755164278052957…79839328562960915199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.705 Γ— 10⁹⁡(96-digit number)
17051755164278052957…79839328562960915201
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
3.410 Γ— 10⁹⁡(96-digit number)
34103510328556105915…59678657125921830399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.410 Γ— 10⁹⁡(96-digit number)
34103510328556105915…59678657125921830401
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
6.820 Γ— 10⁹⁡(96-digit number)
68207020657112211831…19357314251843660799
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:57,969,810 XPMΒ·at block #6,840,683 Β· updates every 60s
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