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Block #2,584,261

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/25/2018, 5:38:07 AM Β· Difficulty 11.2037 Β· 4,258,455 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
06bea810fdf834106d1cd3c850961bb128b25c6aa0c1ce508c288d877f92e5fa
View on Chainz β†—

Height

#2,584,261

Difficulty

11.203701

Transactions

1

Size

200 B

Version

2

Bits

0b3425b8

Nonce

1,872,323,273

Timestamp

3/25/2018, 5:38:07 AM

Confirmations

4,258,455

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

160d87da1930290d191998b0be4af2ca1a0dbde2f1d6bffd07929d14dd8aa022
Transactions (1)
Coinbase160d87da193029…929d14dd8aa022
1 in β†’ 1 out7.9500 XPM110 B
Adqah8zh…1WwoHJ9t
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.

2.687 Γ— 10⁹³(94-digit number)
26873464670534879664…71661034597089896369
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
2.687 Γ— 10⁹³(94-digit number)
26873464670534879664…71661034597089896369
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.687 Γ— 10⁹³(94-digit number)
26873464670534879664…71661034597089896371
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
5.374 Γ— 10⁹³(94-digit number)
53746929341069759329…43322069194179792739
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.374 Γ— 10⁹³(94-digit number)
53746929341069759329…43322069194179792741
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
1.074 Γ— 10⁹⁴(95-digit number)
10749385868213951865…86644138388359585479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.074 Γ— 10⁹⁴(95-digit number)
10749385868213951865…86644138388359585481
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
2.149 Γ— 10⁹⁴(95-digit number)
21498771736427903731…73288276776719170959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.149 Γ— 10⁹⁴(95-digit number)
21498771736427903731…73288276776719170961
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
4.299 Γ— 10⁹⁴(95-digit number)
42997543472855807463…46576553553438341919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.299 Γ— 10⁹⁴(95-digit number)
42997543472855807463…46576553553438341921
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
8.599 Γ— 10⁹⁴(95-digit number)
85995086945711614926…93153107106876683839
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
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