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Block #2,646,397

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/3/2018, 8:26:16 AM Β· Difficulty 11.7494 Β· 4,184,426 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
cacf7c993ff742439d8ca5524923ddc915e0e161dc5f54b51931633d96512904
View on Chainz β†—

Height

#2,646,397

Difficulty

11.749384

Transactions

2

Size

426 B

Version

2

Bits

0bbfd79f

Nonce

180,457,066

Timestamp

5/3/2018, 8:26:16 AM

Confirmations

4,184,426

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

650004f8ee041fe15662b4f6b2fa067279e883a4fdd501cc590bb6bf4823b528
Transactions (2)
Coinbase2715d8bf32ca04…8458daf5fa67fc
1 in β†’ 1 out7.2400 XPM110 B
Adqah8zh…1WwoHJ9t
e6177f458b1774…a5afb943c74898
1 in β†’ 2 out27.7390 XPM226 B
ALajnZMD…GR91zzNVAZ4UnHzJ…PH7NQioA
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.

1.022 Γ— 10⁹⁴(95-digit number)
10224077623668158459…50107503022309987839
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
1.022 Γ— 10⁹⁴(95-digit number)
10224077623668158459…50107503022309987839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.022 Γ— 10⁹⁴(95-digit number)
10224077623668158459…50107503022309987841
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
2.044 Γ— 10⁹⁴(95-digit number)
20448155247336316919…00215006044619975679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.044 Γ— 10⁹⁴(95-digit number)
20448155247336316919…00215006044619975681
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
4.089 Γ— 10⁹⁴(95-digit number)
40896310494672633839…00430012089239951359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.089 Γ— 10⁹⁴(95-digit number)
40896310494672633839…00430012089239951361
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
8.179 Γ— 10⁹⁴(95-digit number)
81792620989345267679…00860024178479902719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.179 Γ— 10⁹⁴(95-digit number)
81792620989345267679…00860024178479902721
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
1.635 Γ— 10⁹⁡(96-digit number)
16358524197869053535…01720048356959805439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.635 Γ— 10⁹⁡(96-digit number)
16358524197869053535…01720048356959805441
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
3.271 Γ— 10⁹⁡(96-digit number)
32717048395738107071…03440096713919610879
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:57,890,717 XPMΒ·at block #6,830,822 Β· updates every 60s
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